文件名:Sup3.3.Nx0.6N0.00 .5%S A3196,A3196,A3196,1,2,0,0,0,24,26,0,0,48 2525204,1929,8812891224195363062,% %T A3196 828026694351577409607569593929 12663160927 9937 61515161600 %N 3A6磁化立方晶格,%R R A3196 JMP 6 1994 297。《整数序列手册》,N.J.A.斯隆,7月2日1994,补充了两个早期补充物理层6,1510,73,πA3193,N001.5,S.A3193,1,2,0,0,16,18,016831414163262649,414148697 6205354,% %T A3193 80176100933535795685675,3024524401240121264098965 16444 64 %%N A3193立方晶格的磁化。%R A3193 JMP 6 297 65。17,1,2,0,2,0,2,0,3,5,9,5,9,4,2,8,5,3,8,1,6,1,6,1,6,1,1,4,4,9,9,9,9,0,7,6,4,9,8,6,2,9,2,9,2,3,4,0,4,9,8,8,8,8,8,1,7,9,2,7,1,5,5,5,3,4,1,8,3,%A2117黎曼ζ函数的3 .% %R A2117 FMR 1 84。物理学报6 1511 15111749668820846324421252566 66 %N A29 76在正方格子上受限行走。%%R A976 JCT 13A 181 72。JWW.I.A.96N90005.5%S S A29 76 1,2,0,5,9,21,42,76PHYSA 6 1511 73. %I A3137 N0011.5 %S A3137 1,2,1,0,1,1,1,2,2,0,2,1,2,2,1,0,0,1,0,1,1,0,2,1,1,0,1,1,1,1,1,2,1, %T A3137 2,0,1,2,1,1,2,2,2,0,0,2,0,1,2,0,2,2,1,0,2,1,1,2,1,2,2,2,0,2,2,1,2,2,2,1 %N A3137 INTEGERS WRITTEN TO BASE 3. %R A3137 %I A3263 N0014.5 %S A3263 1,2,1,0,2,2,0,1,3,2,0,2,3,1,0,3,3,0,2,4,2,0,3,3,0,1,4,3,0,3,5,2,0, %T A3263 4,4,0,2,5,3,0,3,4,1,0,4,4,0,3,6,3,0,5,5,0,2,6,4,0,4,6,2,0,5,5,0,3,6,3,0 %N A3263 REPRESENTATIONS AS A SUM OF LUCAS NUMBERS. %R A3263 BR1 58. %I A2951 N0019.5 %S A2951 1,2,1,1,1,2,1,2,8,1,25,1,5,1,22,1,8,1,1,9,1,1,4,1,2,1,2,1,2,2,1,1, %T A2951 1,1,2,1,6,2,46,1,12,1,32,1,2,3,2,3,55,1,12,3,8,1,1,11,1,4,1,1,1,2,1,1,7 %N A2951 CONTINUED FRACTION EXPANSION OF FIFTH ROOT OF 5. %R A2951 HPR. JSH. %I A3023 N0019.8 %S A3023 1,2,1,1,1,2,3,3,1,6,1,4,4,5,1,3,1,6,2,5,1,4,2,6,2,1,1,14,1,2,5,7,2, %T A3023 3,1,6,2,3,1,13,1,4,6,7,1,5,3,2,3,8,1,12,2,4,2,3,1,10,1,8,2,3,2,11,1,4,3 %N A3023 LENGTH OF ALIQUOT SERIES FOR N. %R A3023 MA5 558. %I A3285 N0027.5 %S A3285 1,2,1,1,2,4,2,1,1,2,2,5,4,2,1,1,2,6,2,6,6,4,2,1,1,2,4,5,2,8,4,4,4, %T A3285 2,1,1,2,2,2,3,2,10,8,6,12,4,2,1,1,2,6,5,6,4,2,6,7,6,4,11,4,2,1,1,2,10,2 %N A3285 PERIOD OF CONTINUED FRACTION FOR SQUARE ROOT OF N. %R A3285 BR2 197. %I A3417 N0027.8 %S A3417 1,2,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,1,14,1,1,16,1,1,18,1,1, %T A3417 20,1,1,22,1,1,24,1,1,26,1,1,28,1,1,30,1,1,32,1,1,34,1,1,36,1,1,38,1,1 %N A3417 CONTINUED FRACTION EXPANSION OF E. %R A3417 PE1 134. %C N0037 N0037 %S N0037 1,2,1,2,2,1,3,2,2,3,1,3,3,2,4,2,3,3,1,4,3,3,5,2,4,4,2,5,3,3,4,1,4, %T N0037 4,3,6,3,5,5,2,6,4,4,6,2,5,5,3,6,3,4,4,1,5,4,4,7,3,6,6,3,8,5,5,7,2,6,6,4 %N N0037 REPRESENTATIONS AS A SUM OF FIBONACCI NUMBERS. %R N0037 FQ 4 305 66. BR1 54. %I A3165 N0041.5 %S A3165 1,2,1,2,2,4,1,5,4,4,4,7,4,8,5,7,8,10,5,10,10,10,9,13,8,14,11,13,14, %T A3165 14,10,17,16,16,13,19,14,20,17,17,20,22,15,22,20,22,21,25,20,24,21,25,26 %N A3165 [N/2] + 1 - NUMBER OF DIVISORS OF N. %R A3165 NE1 186. %Q N0048 N0048 %R N0048 MU4 38. %Q N0049 N0049 %R N0049 MU4 38. %I A3139 N0052.5 %S A3139 1,2,1,3,1,3,2,9,1,10,2,4,3,19,1,20,2,6,4,32,1,21,7,16,7,84,1,85,9, %T A3139 18,11,35,3,161,15,30,6,212,2,214,15,12,19,260,3,154,11,62,31,521,5,129 %N A3139 COPRIME CHAINS. %R A3139 PAMS 16 809 65. %I A2973 N0053.5 %S A2973 1,2,1,3,2,1,3,4,4,2,5,5,4,2,5,3,1,5,6,7,1,4,2,8,5,7,8,1,6,7,8,9,4, %T A2973 9,5,3,10,10,7,6,10,2,5,11,10,5,7,10,12,4,12,9,8,2,11,3,6,13,13,11,1,13 %N A2973 QUADRATIC PARTITIONS OF PRIMES. %R A2973 KK1 243. %Q N0063 N0063 %R N0063 MU4 38. %I A3484 N0063.5 %S A3484 1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,9,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,10,1, %T A3484 2,1,4,1,2,1,8,1,2,1,4,1,2,1,9,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,12,1,2,1,4 %N A3484 HUR10065.5%S S A29 88、1、2、1、4、5、46、37 176、1450、412、125、465、2、6、1、77、34、110、125、1、N、N、A29、A(N)与I(I)模N-I一致,对于所有I .R A29 8SAB。WiZ-RADON函数.%%R A384LAM 131WE2 238。2.5%C A1285 N071%N A1285非重复序列:Tuuer-MaSe序列。%R A1285 GO5 105。JCT13A 90 72. %I A2947 N0074.5 %S A2947 1,2,2,1,3,2,3,1,3,1,30,1,4,1,2,9,6,4,1,1,2,7,2,3,2,1,6,1,1,1,25,1, %T A2947 7,7,1,1,1,1,266,1,3,2,1,3,60,1,5,1,8,5,6,1,4,20,1,4,1,1,14,1,4,4,1,1,1 %N A2947 CONTINUED FRACTION FOR CUBE ROOT OF 4. %R A2947 JRAM 255 122 72. %I A3108 N0076.5 %S A3108 1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,6,6,6,7,7,7,7,7, %T A3108 8,8,8,9,9,9,9,9,10,10,10,11,11,11,12,12,13,13,13,14,14,14,15,15,17,17 %N A3108 PARTITIONS INTO CUBES. %R A3108 HPR. %I A3036 N0079.3 %S A3036 1,2,2,2,2,4,2,4,5,5,6 %N A3036 SIMPLICIAL ARRANGEMENTS. %R A3036 GR3 7. %I A3016 N0079.5 %S A3016 1,2,2,2,3,2,2,2,4,2,2,2,2,4,2,2,2,2,3,4,2,2,2,2,2,2,4,2,2,2,2,2,2, %T A3016 4,4,2,2,2,2,2,2,2,2,4,2,2,2,2,2,2,2,2,2,4,4,2,2,2,2,2,2,2,2,2,4,2,2,2,3 %N A3016 NUMBER OF OCCURRENCES OF N AS A BINOMIAL COEFFICIENT. %R A3016 AMM 78 385 71.OG1 96. %I A3050 N0079.8 %S A3050 1,2,2,2,3,3,4,3,4,3,6,4,5,6,6,4,7,5,8,8,7,5,12 %N A3050 REGULAR HAMILTONIAN MAPS ON THE TORUS. %R A3050 DM 4 216 73. %C N0082 N0082 %N N0082 [(2**N)/N]. %R N0082 %I A3434 N0084.5 %S A3434 1,2,2,3,2,3,3,3,3,4,3,4,3,4,4,5,3,4,4,4,4,5,4,5,4,4,4,5,4,5,5,5,5, %T A3434 5,4,5,4,5,5,6,4,5,5,5,5,6,5,5,5,6,5,6,4,6,5,5,5,6,5,6,5,5,6,6,5,6,6,6,5 %N A3434 RELATED TO PHI(N). %R A3434 BAMS 35 837 29. %I A3105 N0089.5 %S A3105 1,2,2,3,3,3,4,5,6,7,8,9,10,12,14,16,18,20,23,26,30,34,38,42,47,53, %T A3105 60,67,74,82,91,102,114,126,139,153,169,187,207,228,250,274,301,331,364 %N A3105 PARTITIONS INTO PARTS 6N+1 OR 6N-1. %R A3105 HPR. %I A3313 N0089.8 %S A3313 1,2,2,3,3,4,3,4,4,5,4,5,5,5,4,5,5,6,5,6,6,6,5,6,6,6,6,7,6,7,5,6,6, %T A3313 7,6,7,7,7,6,7,7,7,7,7,7,8,6,7,7,7,7,8,7,8,7,8,8,8,7,8,8,8,6,7,7,8,7,8,8 %N A3313 MINIMUM MULTIPLICATIONS TO COMPUTE X**N. %R A3313 KN1 2 403. %I A3106 N0092.5 %S A3106 1,2,2,3,3,4,4,6,6,8,9,11,12,15,16,20,22,26,29,35,38,45,50,58,64,75, %T A3106 82,95,105,120,133,152,167,190,210,237,261,295,324,364,401,448,493,551 %N A3106 PARTITIONS INTO PARTS 5N+2 OR 5N+3. %R A3106 HPR. %I A3114 N0093.2 %S A3114 1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,26,31,35,41,46,54,61,70,79, %T A3114 91,102,117,131,149,167,189,211,239,266,299,333,374,415,465,515,575,637 %N A3114 PARTITIONS INTO PARTS 5N+1 OR 5N-1. %R A3114 DHL. %I A3113 N0093.5 %S A3113 1,2,2,3,3,5,5,7,8,10,11,15,16,20,23,28,31,38,42,51,57,67,75,89,99, %T A3113 115,129,149,166,192,213,244,272,309,344,391,433,489,543,611,676,760,839 %N A3113 EXPANSION OF A PERMANENT. %R A3113 DHL. %I A3002 N0097.5 %S A3002 1,2,2,3,4,4,4,4,5,5,6,6,7,8,8,8,8,8,8,9,9,9,9,10,10,11,11,11,11,12, %T A3002 12,13,13,13,13,14,14,14,14,15,16,16,16,16,16,16,16,16,16,16,17,17,17 %N A3002 3-FREE SEQUENCES. %R A3002 MTAC 26 768 72. %I A3073 N0100.5 %S A3073 1,2,2,3,4,5,7,9,11,14,18,23,29,38,47,59,76,95,120,154,191,241,310, %T A3073 383,483,620,767,968,1242,1535,1937,2486,3071,3875,4972,6143,7752,9946 %N A3073 A NONLINEAR RECURRENCE. %R A3073 KN1 3 208. %I A3179 N0103.5 %S A3179 1,2,2,3,4,7,9,16,25,55 %N A3179 SELF-DUAL CODES. %R A3179 PS1. %I A2948 N0111.5 %S A2948 1,2,2,4,3,3,1,5,1,1,4,10,17,1,14,1,1,3052,1,1,1,1,1,1,2,2,1,3,2,1, %T A2948 13,5,1,1,1,13,2,41,1,4,12,1,5,2,7,1,1,3,33,2,1,1,1,1,1,1,3,2,2,1,15,12 %N A2948 CONTINUED FRACTION EXPANSION OF CUBE ROOT OF 5. %R A2948 JRAM 255 124 72. %I A3000 N0123.5 %S A3000 1,2,2,4,6,12,20,40,74,148,284,568,1116,2232,4424,8848,17622,35244, %T A3000 70340,140680,281076,562152,1123736,2247472,4493828,8987656,17973080 %N A3000 A(N) = 2A(N-1) IF N ODD, 2A(N-1) - A(N/2) IF N EVEN. %R A3000 %I A2990 N0131.5 %S A2990 1,2,2,5,9,19,38,86,188,439,1026,2472,5997,14835,36964,93246,236922, %T A2990 607111,1565478,4062797,10599853,27797420,73224806,193709710,514406793 %N A2990 TREES WITH A FORBIDDEN LIMB. %R A2990 HA7 297. %I A3228 N0131.8 %S A3228 1,2,2,5,9,21,43,101,226,556,1333,3365,8500,22007,57258,151264, %T A3228 401761,1077063,2902599,7871250,21440642,58672581,161155616,444240599 %N A3228 ENDPOINTS IN TREES. %R A3228 HA9. %I A3178 N0133.5 %S A3178 1,2,2,6,8,26 %N A3178 INDECOMPOSABLE SELF-DUAL CODES. %R A3178 PS1. %I A3181 N0141.5 %S A3181 1,2,2,8,68,3904,37329264 %N A3181 NONDEGENERATE BOOLEAN FUNCTIONS. %R A3181 MU4 38. %Q N0142 N0142 %R N0142 MU4 38. %Q N0145 N0145 %R N0145 MU4 38. %I A3090 N0146.5 %S A3090 1,2,2,12,147 %N A3090 SPECIES OF LATIN SQUARES. %R A3090 HA8 231. %I A3110 N0150.5 %S A3110 1,2,2,108,2028,32870,1213110 %N A3110 SPECIAL PERMUTATIONS. %R A3110 JNT 5 48 73. %I A3315 N0155.3 %S A3315 1,2,3,1,2,3,4,5,1,2,3,2,3,4,5,1,2,3,4,5,3,4,5,2,1,2,3,2,3,4,2,3,2, %T A3315 3,4,1,2,3,4,3,4,3,2,2,3,4,3,4,1,2,3,2,3,4,5,6,2,3,3,3,4,5,2,1,2,3,4,2,3 %N A3315 REPRESENTING N AS SUM OF INCREASING POWERS. %R A3315 BIT 12 342 72. %I A3270 N0155.5 %S A3270 1,2,3,1,3,2,3,1,2,3,2,1,3,1,2,1,3,2,3,1,2,3,2,1,2,3,1,2,1,3,2,3,1, %T A3270 3,2,1,3,1,2,3,2,1,2,3,1,3,2,1,3,1,2,1,3,2,3,1,2,3,2,1,2,3,1,2,1,3,2,3,1 %N A3270 A NONREPETITIVE SEQUENCE. %R A3270 YAG 2 204. JCT 13A 90 72. %I A2946 N0155.8 %S A2946 1,2,3,1,4,1,5,1,1,6,2,5,8,3,3,4,2,6,4,4,1,3,2,3,4,1,4,9,1,8,4,3,1, %T A2946 3,2,6,1,6,1,3,1,1,1,1,12,3,1,3,1,1,4,1,6,1,5,1,2,1,3,3,11,8,1,139,8,2,8 %N A2946 CONTINUED FRACTION EXPANSION OF CUBE ROOT OF 3. %R A2946 JRAM 255 120 72. %I A3051 N0160.5 %S A3051 1,2,3,2,3,3,5,4,4,3,8,4,5,6,16,4,8,5,10,8,7,5,15 %N A3051 REGULAR MAPS ON THE TORUS. %R A3051 DM 4 216 73. %I A3063 N0164.2 %S A3063 1,2,3,3,4,4,5,4,5,5,6,5,6,6,6,5,6,6,7,6,7,7,7,6,7,7,7,7,8,7,8,6,7, %T A3063 7,8,7,8,8,8,7,8,8,8,8,8,8,9,7,8,8,8,8,9,8,9,8,9,9,9,8,9,9,9,7,8,8,9,8,9 %N A3063 SHORTEST ADDITION CHAIN FOR N. %R A3063 KN1 2 403. %I A3003 N0164.5 %S A3003 1,2,3,3,4,5,5,6,7,8,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16, %T A3003 17,17,18,18,18,19,20,20,20,21,21,21,22,22,22,23,23,24,24,24,25,25,26,26 %N A3003 4-FREE SEQUENCES. %R A3003 MTAC 26 768 72. %I A3324 N0165.5 %S A3324 1,2,3,4,1,4,3,2,1,2,3,2,1,4,3,4,1,2,3,4,1,4,3,4,1,2,3,2,1,4,3,2,1, %T A3324 2,3,4,1,4,3,2,1,2,3,2,14、3、3、2、1、2、3、4、1、4、3、4、1、2、3、2、1、4、3、4、1、2、3、4、1、N、N、A33 24为非重复序列。JCT 13A 90 72. %I A3160 N0166.2 %S A3160 1,2,3,4,4,4,5,5,5,6,6,6,7,8,9,9,9,10,11,12,12,12,13,14,15,15,15,16, %T A3160 16,16,17,17,17,18,19,20,20,20,21,21,21,22,22,22,23,24,25,25,25,26,26,26 %N A3160 A SELF-GENERATING SEQUENCE. %R A3160 FQ 10 507 72. %I A3004 N0166.5 %S A3004 1,2,3,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,16,16,16,16,17,18,18, %T A3004 19,20,21,21,22,22,23,24,24,25,26,27,28,28,29,30,31,32,32,32,32,32,33,33 %N A3004 5-FREE SEQUENCES. %R A3004 MTAC 26 768 72. %I A3005 N0167.5 %S A3005 1,2,3,4,5,5,6,7,8,9,9,10,11,12,13,13,14,15,16,17,17,18,19,20,21,22, %T A3005 22,22,23,23,23,24,25,25,26,27,28,28,29,30,31,31,31,32,33,34,34,35,36,37 %N A3005 6-FREE SEQUENCES. %R A3005 MTAC 26 768 72. %C N0176 N0176 %N N0176 EULER'S IDONEAL OR SUITABLE NUMBERS (A FINITE SEQUENCE). %R N0176 BO1 427. ELM 21 83 66. %I A3100 N0178.3 %S A3100 1,2,3,4,5,6,7,8,9,19,18,17,16,15,14,13,12,11,10,20,21,22,23,24,25, %T A3100 26,27,28,29,39,38,37,36,35,34,33,32,31,30,40,41,42,43,44,45,46,47,48,49 %N A3100 A GRAY CODE FOR THE INTEGERS. %R A3100 MAG 50 122 66. %I A2998 N0178.5 %S A2998 1,2,3,4,5,6,7,8,9,190,209,48,247,266,195,448,476,198,874,3980,399, %T A2998 2398,1679,888,4975,1898,999,7588,4988,39990,8959,17888,42999,28798,57995 %N A2998 SMALLEST MULTIPLE OF N WHOSE DIGITS SUM TO N. %R A2998 %I A3045 N0178.8 %S A3045 1,2,3,4,5,6,7,8,10,12,14,16,19,21,23,25,30,44,46,48,50,55,65,73,74, %T A3045 77,84,86,91,95,97,114,122,123,126 %N A3045 A SELF-GENERATING SEQUENCE. %R A3045 JCT 12A 65 72. %I A3103 N0178.9 %S A3103 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26, %T A3103 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51 %N A3103 NO CUBES. %R A3103 AMM 61 458 54. %I A3401 N0182.3 %S A3401 1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,32,34,40,48,51,60,64,68,80,% %T A3401 85,961021201016017190220424025525625727 23 20340404 4%%A3401多边形,用尺和罗盘构成。%R R A3401 GA4 460。VDW 1 187.BE3 183. %I A3044 N0182.5 %S A3044 1,2,3,4,5,6,8,10,12,15,17,19,29,31,33,43,47,51,54,58,68,69,78,79, %T A3044 86,95,99,110,113,117,133 %N A3044 A SELF-GENERATING SEQUENCE. %R A3044 JCT 12A 64 72. %I A3520 N0182.7 %S A3520 1,2,3,4,5,6,8,11,15,20,26,34,45,60,80,106,140,185,245,325,431,571, %T A3520 756,1001,1326,1757,2328,3084,4085,5411,7168,9496,12580,16665,22076,29244 %N A3520 A(N) = A(N-1) + A(N-5). %R A3520 BR1 119. %I A3413 N0187.5 %S A3413 1,2,3,4,5,7,9,12,15,19,24,31,40,52,67,86,110,141,181,233,300,386, %T A3413 496,637,818,1051,1351,1737,2233,2870,3688,4739,6090,7827,10060,12930 %N A3413 FROM A NIM-LIKE GAME. %R A3413 GU5. %I A3269 N0188.3 %S A3269 1,2,3,4,5,7,10,14,19,26,36,50,69,95,131,181,250,345,476,657,907, %T A3269 1252,1728,2385,3292,4544,6272,8657,11949,16493,22765,31422,43371,59864 %N A3269 A(N) = A(N-1) + A(N-4). %R A3269 BR1 119. %I A3037 N0188.5 %S A3037 1,2,3,4,5,7,11,13,21,23,41,43,71,94,139,211,215,431,863 %N A3037 COMPLICATED NUMBERS. %R A3037 BSU. %I A3271 N0188.8 %S A3271 1,2,3,4,5,9,16,17,41,83,113,137,257,773,977,1657,2048,2313,4001, %T A3271 5725,7129,11117,17279,19897,22409,39283,43657,55457 %N A3271 RELATED TO ITERATES OF UNITARY TOTIENT FUNCTION. %R A3271 MTAC 28 302 74. %Q A0667 N0189 %R A0667 PNAS 68 2320 71. %I A3247 N0191.5 %S A3247 1,2,3,4,6,7,8,9,10,11,12,13,15,16,17,18,19,21,22,23,24,25,26,27,28, %T A3247 30,31,32,33,34,36,37,38,40,41,42,43,44,46,47,48,49,50,51,52,53,55,56,57 %N A3247 RELATED TO FIBONACCI REPRESENTATIONS. %R A3247 FQ 11 385 73. %I A2982 N0195.5 %S A2982 1,2,3,4,6,7,12,14,30,32,33,38,94 %N A2982 FACTORIAL(N) - 1 IS PRIME. %R A2982 MTAC 26 568 72. %I A2984 N0200.5 %S A2984 1,2,3,4,6,8,10,13,16,20,24,28,33,38,44,50,57,64,72,80,88,97,106, %T A2984 116,126,137,148,160,172,185,198,212,226,241,256,272,288,304,321,338,356 %N A2984 A(N) = A(N-1) + [SQUARE ROOT OF A(N-1)]. %R A2984 %I A3107 N0200.8 %S A3107 1,2,3,4,6,8,10,14,17,22,27,33,41,49,59,71,83,99,115,134,157,180, %T A3107 208,239,2723 12353554059536367417178099931 1021219135050%N A3107划分成斐波那契部分。AT1 249。JCT12A 39 72。AMM 80 919,73。PC1 2 13-7 74. %I A3412 N0201.3 %S A3412 1,2,3,4,6,8,11,14,18,24,32,43,54,68,86,110,142,185,239,307,393,503, %T A3412 645,830,1069,1376,1769,2272,2917,3747,4816,6192,7961,10233,13150,16897 %N A3412 FROM A NIM-LIKE GAME. %R A3412 GU5. %I A3411 N0201.6 %S A3411 1,2,3,4,6,8,11,15,21,29,40,55,76,105,145,200,276,381,526,726,1002, %T A3411 1383,1909,2635,3637,5020,6929,9564,13201,18221,25150,34714,47915,66136 %N A3411 FROM A NIM-LIKE GAME. %R A3411 GU5. %I A3143 N0206.5 %S A3143 1,2,3,4,6,9,13,19,27,38,54,77,109,155,219,310,438,621,877,1243, %T A3143 1755,2486,3510,4973,7021,9947,14043,19894,28086,39789,56173,79579,112347 %N A3143 A(2N) = [17.2**N/14], A(2N+1) = [12.2**N/7]. %R A3143 KN1 3 207. %C N0208 N0208 %N N0208 FIBONACCI NUMBERS + 1. %R N0208 %I A3099 N0209.5 %S A3099 1,2,3,4,6,11,22,43,79,137,231,397,728,1444,3018,6386,13278,26725, %T A3099 51852,97243,177671,320286,579371,1071226,2053626,4098627,8451288 %N A3099 SUM OF C(N,K**2). %R A3099 HWG. %I A3508 N0211.5 %S A3508 1,2,3,4,7,8,11,12,18,24,30,41,42,55,72,78,97,98,108,114,139,140, %T A3508 155,192,198,215,264,281,282,335,408,431,432,438,517,576,582,685,828,857 %N A3508 A(N) = A(N-1) + SUM OF PRIME FACTORS OF A(N-1). %R A3508 MMAG 48 57 75. %I A3272 N0212.3 %S A3272 1,2,3,4,8,9,10,11,12,16,17,18,19,25,26,27,32,33,35,36,40,42,43,44, %T A3272 48,49,50,51,57,58,59,64,66,67,68,72,73,74,75,76,81,82,83,89,90,91,97,98 %N A3272 NONCONGRUENT NUMBERS. %R A3272 MTAC 28 305 74. %I A2971 N0212.5 %S A2971 1,2,3,4,8,9,11,12,13,14,16,17,18,21,23,26,29,34,36,37,38,47,48,49, %T A2971 51,53,54,56,62,63,66,67,68,69,73,74,77,79,82,83,91,99,101,102,103,107 %N A2971 (2N)**2 + 25 IS PRIME. %R A2971 KK1 1. %Q A0032 N0213 %R A0032 PNAS 68 2320 71. %I A3251 N0222.5 %S A3251 1,2,3,5,6,7,8,9,10,12,13,14,16,17,18,19,20,21,23,24,25,27,28,30,31, %T A3251 32,34,35,36,37,38,39,41,42,43,45,46,47,48,49,50,52,53,54,55,56,57,59,60 %N A3251 RELATED TO FIBONACCI REPRESENTATIONS. %R A3251 FQ 11 385 73. %I A3172 N0225.3 %S A3172 12、3、5、6、7、11、13、14、17、22、23、29、31、37、37、38、41、43、47、47、53、8、T、A3172、57、59、61、62、67、69、71,73、77、83、86、893、93、94、97、1010、79、109、131、118、18、N、A3172、具有唯一因式分解的实二次域。%R A3172 Ba6 1。Bo1 422.ST5 296πA3174 N0225.8%S S A3174,1,2,3,5,6,7,11,13,17,19,21,29,33,37,41,57,73.7%.3%A3174实二次欧氏场(有限序列)。AMM 75 948,68。ST5 294. %I A3238 N0229.5 %S A3238 1,2,3,5,6,10,11,16,19,26 %N A3238 ACHIRAL PLANTED TREES. %R A3238 HA10. %I A3258 N0231.5 %S A3258 1,2,3,5,7,8,10,12,13,15,16,18,20,21,23,24,26,28,29,31,33,34,36,37, %T A3258 39,41,42,44,46,47,49,50,52,54,55,57,58,60,62,63,65,67,68,70,71,73,75,76 %N A3258 RELATED TO FIBONACCI REPRESENTATIONS. %R A3258 FQ 11 386 73. %C N0232 N0232 %N N0232 (2N)**2 + 1 IS PRIME. %R N0232 KR1 1 11. KK1 1。OG1 116 .0%C N023 8N023 8%N N023 8堆叠,或平面分区。%%R N023 8 PCPS 47 686 686。QJMO 23 153 72. %I A3410 N0240.3 %S A3410 1,2,3,5,7,10,15,22,32,47,69,101,148,217,318,466,683,1001,1467,2150, %T A3410 3151,4618,6768,9919,14537,21305,31224,45761,67066,98290,144051,211117 %N A3410 FROM A NIM-LIKE GAME. %R A3410 GU5. %I A3277 N0240.5 %S A3277 1,2,3,5,7,11,13,15,17,19,23,29,31,33,35,37,41,43,47,51,53,59,61,65, %T A3277 67,69,71,73,77,79,83,85,87,89,91,95,97,101,103,107,109,113,115,119,123 %N A3277 N AND PHI(N) ARE RELATIVELY PRIME. %R A3277 JIMS 12 75 48. %I A3309 N0242.3 %S A3309 1,2,3,5,7,11,13,17,23,25,29,37,41,43,47,53,61,67,71,77,83,89,91,97, %T A3309 107,115,119,121,127,131,143,149,157,161,173,175,179,181,193,209,211,221 %N A3309 GENERATED BY A SIEVE. %R A3309 PC1 2 13-6 74. %I A3459 N0242.5 %S A3459 1,2,3,5,7,11,13,17,31,37,71,73,79,97,113,131,199,311,337,373,733, %T A3459 919,991 %N A3459 EVERY PERMUTATION OF DIGITS IS A PRIME. %R A3459 MMAG 47 233 74. %I A3064 N0245.5 %S A3064 1,2,3,5,7,11,19,29,47,71,127,191,379,607,1087,1903 %N A3064 SMALLEST NUMBER WITH ADDITION CHAIN OF LENGTH N. %R A3064 KN1 2 416. %I A2965 N0247.5 %S A2965 1,2,3,5,7,12,17,29,41,70,99,169,239,408,577,985,1393,2378,3363, %T A2965 5741,8119,13860,19601,33461,47321,80782,114243,195025,275807,470832 %N A2965 CONVERGENTS TO SQUARE ROOT OF 2. %R A2965 JALG 20 173 72. %Q A0043 N0248 %R A0043 PNAS 68 2319 71. %C N0253 N0253 %N N0253 STACKS, OR PLANAR PARTITIONS. %R N0253 PCPS 47 686 51. QJMO 23 153 72. %I A3476 N0260.2 %S A3476 1,2,3,5,9,15,25,43,73,123,209,355,601,1019,1729,2931,4969,8427, %T A3476 14289,24227,41081,69659,118113,200275,339593,575819,976369,1655555 %N A3476 A(N) = A(N-1) + 2A(N-3). %R A3476 DA4. %I A3065 N0260.5 %S A3065 1,2,3,5,9,15,26,44,78,136,246,432 %N A3065 RELATED TO LENGTH OF ADDITION CHAINS. %R A3065 KN1 2 417. %C N0261 N0261 %N N0261 PARTITIONS INTO POWERS OF 1/2, OR BINARY ROOTED TREES. %R N0261 EMS 11 22459. ST3IC 21、482、72、β%C N0267、N0267、%N、N0267烷烃、或石蜡。% %R N0267 JACS 54 2919 32。BS1 201。GTA 257 .0%D A05250N8268i,A318N02685%S S A32 18,1,2,3,5,9,18,42 % N A32 18的阈值函数的权重。% %R A32 18MU4 268。I A34 32 N0268 8 %S S A32 32 1,2,3,5,9,32,561443201463645 947 7 7%7 N % A34 32(0,1)-矩阵的最大行列式。% %R A34 32 ZAMM 42 T21 62。MZT 83 127 64.AMM 79 626 72. %I A2991 N0270.5 %S A2991 1,2,3,5,10,21,43,97,215,503,1187,2876,7033,17510,43961,111664, %T A2991 285809,737632,1915993,5008652,13163785,34774873,92282214,245930746 %N A2991 TREES WITH A FORBIDDEN LIMB. %R A2991 HA7 297. %Q N0272 N0272 %R N0272 MU4 38. %I A3504 N0272.5 %S A3504 1,2,3,5,10,28,154,3520,1551880,267593772160,7160642690122633501504, %T A3504 4661345794146064133843098964919305264116096 %N A3504 A(N+1) = (1 + A(1)**2 + ... + A(N)**2)/N. %R A3504 HWL. %I A3428 N0276.5 %S A3428 1,2,3,5,12,22,47,94,201,417,907,1948,4289,9440,21063,47124,106377, %T A3428 240980,549272,1256609,2888057,6660347,15416623,35794121,83362301 %N A3428 TREES BY STABILITY INDEX. %R A3428 CM2 51. %I A3421 N0282.5 %S A3421 1,2,3,6,7,10,19,31,34,46,79,106,151,211,214,274,331,394,631,751, %T A3421 919,991,1054,1486,1654 %N A3421 EXTREME VALUES OF DIRICHLET SERIES. %R A3421 PSPM 24 279 73. %I A3405 N0284.5 %S A3405 1,2,3,6,8,13,19,30,41,59,80,113,149,202,264,350,447,578,730,928, %T A3405 1155,1444,1777,2193,2667,3249,3915,4721,5635,6728,7967,9432,11083,13016 %N A3405 CERTAIN PARTIALLY ORDERED SETS OF INTEGERS. %R A3405 LMS13 123. %I A3244 N0286.5 %S A3244 1,2,3,6,9,16,23,35,51,72 %N A3244 ACHIRAL TREES. %R A3244 HA10. %I A3243 N0287.5 %S A3243 1,2,3,6,9,19,30,61,99,208 %N A3243 PARTIALLY ACHIRAL TREES. %R A3243 HA10. %I A3237 N0291.5 %S A3237 1,2,3,6,10,19,33,62,110,204 %N A3237 PARTIALLY ACHIRAL PLANTED TREES. %R A3237 HA10. %Q N0294 N0294 %R N0294 JCT 1 299 66. %I A3214 N0295.1 %S A3214 1,2,3,6,10,20,37,76,152,320,672,1454,3154,6959,15439,34608,77988, %T A3214 176985,403510,924683,2127335,4913452,11385955,26468231,61700232 %N A3214 BINARY FORESTS. %R A3214 ME2. %I A2988 N0295.2 %S A2988 1,2,3,6,10,21,39,82,167,360,766,1692,3726,8370,18866,43029,98581, %T A2988 227678,528196,1232541,2888142,6798293,16061348,38086682,90607902 %N A2988 TREES WITH A FORBIDDEN LIMB. %R A2988 HA7 297. %I A2992 N0295.3 %S A2992 1,2,3,6,10,22,45,102,226,531,1253,3044,7456,18604,46798,119133, %T A2992 305567,790375,2057523,5390759,14200122,37598572,100005401,267131927 %N A2992 TREES WITH A FORBIDDEN LIMB. %R A2992 HA7 297. %I A3479 N0295.4 %S A3479 1,2,3,6,11,18,31,54,91,154,263,446,755,1282,2175,3686,6251,10602, %T A3479 17975,30478,51683,87634,148591,251958,427227,724410,1228327,2082782 %N A3479 FROM FOLDING A STRIP OF PAPER. %R A3479 DA4. %I A2985 N0295.5 %S A2985 1,2,3,6,11,20,36,64,108,179,292,464,727,1124,17在轮子中,793%%N A29 85棵树。14258538665724,%%T A985 8418122908302571336898264268837 105831414917820936429IC 21 481 72. %C N0297 N0297 %S N0297 1,2,3,6,11,22,42,84,165,330,654,1308,2605,5210,10398,20796,41550, %T N0297 83100,166116,332232,664299,1328598,2656866,5313732,10626810,21253620 %N N0297 A(2N) = 2A(2N-1), A(2N+1) = 2A(2N) - A(N). %R N0297 CMB 13 108 70. %I A3317 N0302.5 %S A3317 1,2,3,6,12,28,68 %N A3317 MINIMAL BLOCKS WITH N NODES. %R A3317 NBS 77B 56 73. %I A2995 N0304.5 %S A2995 1,2,3,6,14,34,95,280,854,2694 %N A2995 PLANE TREES. %R A2995 CRB 110. εq n0306 n0306 r n0306MU4 38 .i %A3040N03065%,S A3040,1,2,3,6,16,35,902167610724798929,828,41153152,% %T A3040,77305016336636624249420600,16939 1845 466865 40825421588568%n A3040对称群的最大不可约特征。%R A3040 LI1 265。HA10I A3183N03068%S S A3183,1,32.6171712822.0%N3A3183布尔函数。% %R A3183 MU4 38。π%N0308 N0308%%R N0308 MU4 38。MTAC 14110 60MTAC 26 569 72. %I A3307 N0313.3 %S A3307 1,2,3,7,8,12,20,23,27,35,56,62,68,131,222 %N A3307 2.3**N - 1 IS PRIME. %R A3307 MTAC 26 997 72. %I A3308 N0313.8 %S A3308 1,2,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99, %T A3308 105,111,115,127,129,133,135,141,151,159,163,169,171,189,193,195,201,205 %N A3308 LUCKY NUMBERS. %R A3308 MMAG 29 119 55. OG1 99。PC1 2 13-7 74. %I A3173 N0315.5 %S A3173 1,2,3,7,11,19,43,67,163. %N A3173 IMAGINARY QUADRATIC FIELDS WITH UNIQUE FACTORIZATION (A FINITE SEQUENCE). %R A3173 ST5 295. %I A3509 N0316.5 %S A3509 1,2,3,7,13,21,31 %N A3509 A PROBLEM IN (0,1)-MATRICES. %R A3509 AMM 81 1113 74. %I A3120 N0317.5 %S A3120 1,2,3,7,13,31,66,159 %N A3120 TREES OF VALENCY 1. %R A3120 DM 5 197 73. %C N0318 N0318 %N N0318 ALKYL DERIVATIVES OF ACETYLENE. %R N0318 JACS 55 253 33. 2,3,7,15,35,81195,%AN,A300,876,73,ε%N0321,N0321,N0321,1,2,3,7,16,54,2433,1131,20181877,2423,29,1228,88,193064,%,T N0321,36330570441941940401534,1967196148329,407969%,N N0321欧拉图或两个图。% %R N0321 KNAW 69 339 66。GTA 255 .I A300 6N0319.5%S S A300 6 1PTGT 150。VE1 6 46 70.MR 44 44(6557)72。HA8 117。SE4。MS1. %C N0323 N0323 %S N0323 1,2,3,7,21,49,165,549 %N N0323 ALTERNATING AND NONALTERNATING KNOTS. %R N0323 TA1 1 %Q N0324 N0324 %R N0324 MU4 38. %Q N0332 N0332 %R N0332 BIT 13 371 73. %I A2958 N0332.5 %S A2958 1,2,3,8,12,15,27,48,89 %N A2958 2.25**N - 1 IS PRIME. %R A2958 PL2 2 568 71. %I A3473 N0333.5 %S A3473 1,2,3,8,15,24,49,128,189,480,1023,1536,4095,6272,10125,32768,65025, %T A3473 96768,262143,491520,583443,2095104,4190209,6291456,15728625,33546240 %N A3473 GENERALIZED PHI FUNCTION. %R A3473 MTAC 28 1168 74. %I A3096 N0338.5 %S A3096 1,2,3,8,63,3968,15745023,247905749270528, %T A3096 61457260521381894004129398783 %N A3096 A(N) = A(N-1)**2 - 1. %R A3096 FQ 11 430 73. %I A3140 N0338.8 %S A3140 1,2,3,9,10,19,20,32,84,85,161,212,214,260,521,818,820,1189,1406, %T A3140 1415,2005,2375,3351,5698,6122,6141,6600,6623,7270 %N A3140 COPRIME CHAINS. %R A3140 PAMS 16 809 65. %C N0339 N0339 %S N0339 1,2,3,9,20,75,262,1117,4783,21971,102249,489077,2370142,11654465, %T N0339 56916324290696139413413417174171732653269220720796194998%%N 0399多边形的解剖。%%R N033 9 BAMS 54 359 359。REA1. %I A2981 N0342.5 %S A2981 1,2,3,11,27,37,41,73,77 %N A2981 FACTORIAL(N) + 1 IS PRIME. %R A2981 MTAC 26 567 72. %I A3455 N0342.8 %S A3455 1,2,3,11,29,122,479,2113,9369,43392,203595,975563,4736005,23296394, %T A3455 115811855,581324861,2942579633,15008044522,77064865555,398150807179 %N A3455 DISSECTIONS OF A POLYGON. %R A3455 REA1. %I A3221 N0346.5 %S A3221 1,2,3,24,130,930,7413,66752,667476,7342290,88107415,1145396472, %T A3221 16035550518,240533257874,3848532125865,65425046139840,1177650830516968 %N A3221 EVEN DERANGEMENTS. %R A3221 AMM 79 394 72. %I A3233 N0354.3 %S A3233 1,2,4,5,6,7,9,10,12,13,14,15,17,18,20,22,23,25,26,27,28,30,31,33, %T A3233 34,35,36,38,39,40,41,43,44,46,47,48,49,51,52,54,56,57,59,60,61,62,64,65 %N A3233 RELATED TO FIBONACCI REPRESENTATIONS. %R A3233 FQ 11 385 73. %I A3511 N0354.5 %S A3511 1,2,4,5,6,8,9,10,12,13,15,16,17,19,20,21,23,24,25,27,28,30,31,32, %T A3511 34,35,36,38,39,40,42,43,45,46,47,49,50,51,53,54,56,57,58,60,61,62,64,65 %N A3511 A BEATTY SEQUENCE. %R A3511 DM 2 338 72. %I A3232 N0354.8 %S A3232 1,2,4,5,6,8,9,11,12,13,15,16,17,19,20,22,23,24,26,27,29,30,31,33, %T A3232 34,35,37,38,40,41,42,44,45,46,48,49,51,52,53,55,56,58,59,60,62,63,64,66 %N A3232 RELATED TO A BEATTY SEQUENCE. %R A3232 FQ 11 347 73. %I A3306 N0355.5 %S A3306 1,2,4,5,6,9,16,17,30,54,57,60,65,132,180,320 %N A3306 2.3**N + 1 IS PRIME. %R A3306 MTAC 26 996 72. %C N0356 N0356 %S N0356 1,2,4,5,7,8,9,11,12,14,15,16,18,19,21,22,24,25,26,28 %N N0356 A BEATTY SEQUENCE. %R N0356 CMB 2 188 59. FQ 10 487 72. %I A3253 N0357.5 %S A3253 1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,24,25,27,28,30,31,33,34,36, %T A3253 37,39,40,42,43,45,46,48,49,51,52,54,55,57,58,60,62,63,65,66,68,69,71,72 %N A3253 RELATED TO FIBONACCI REPRESENTATIONS. %R A3253 FQ 11 386 73. %C N0363 N0363 %S N0363 1,2,4,5,8,10,14,15,16,21,22,25,26,28,33,34,35,36,38,40,42,46,48,49, %T N0363 50,53,57,60,62,64,65,70,77,80,81,83,85,86,90,91,92,100,104,107,108,116 %N N0363 PRIME NUMBERS OF MEASUREMENT, A SELF-GENERATING SEQUENCE. %R N0363 PCPS 21654 23. AMM 75 80,68。AND1. %I A3278 N0364.5 %S A3278 1,2,4,5,10,11,13,14,28,29,31,32,37,38,40,41,82,83,85,86,91,92,94, %T A3278 95,109,110,112,113,118,119,121,122,244,245,247,248,253,254,256,257,271 %N A3278 A(N) = SMALLEST NUMBER SO THAT NO 3 OF A(1),...,A(N) ARE IN ARITHMETIC PROGRESSION. %R A3278 JLMS 11 263 36. %I A2959 N0367.5 %S A2959 1,2,4,5,14,24,29,36,46,80 %N A2959 2.7**N - 1 IS PRIME.569 71. %R A2959 PL2 2 %I A3035 N0369.5 %S A3035 1,2,4,6,7,10,12,16,19 %N A3035 MAXIMUM NUMBER OF LINES EACH CONTAINING 3 POINTS. %R A3035 GR3 22. GMD 2 39974. %I A3254 N0369.8 %S A3254 1,2,4,6,8,9,10,12,14,15,17,19,21,23,24,25,27,29,31,33,34,35,37,39, %T A3254 40,42 %N A3254 RELATED TO FIBONACCI REPRESENTATIONS. %R A3254 FQ 11 385 73. %I A3066 N0373.5 %S A3066 1,2,4,6,9,12,15,19,23,27,31,35,40,45,50,55,60,65,70,75,80,86 %N A3066 PROBLIMES. %R A3066 AMM 80 677 73. %I A3402 N0375.5 %S A3402 1,2,4,6,9,14,19,27,37,49,64,84,106,134,168,207,253,309,371,445,530, %T A3402 626,736,863,1003,1163,1343,1543,1766,2017,2291,2597,2935,3305,3712,4161 %N A3402 CERTAIN TRIANGULAR ARRAYS OF INTEGERS. %R A3402 LMS13 112. %I A3151 N0389.2 %S A3151 1,2,4,7,9,12,14,16,19,21,24,26,28,31,33,36,38,41,43,45,48 %N A3151 A BEATTY SEQUENCE. %R A3151 FQ 10 487 72. %I A3067 N0389.3 %S A3067 1,2,4,7,10,13,17,21,25,29,34,39,44,49,54,59,64,69,74,79,84,90 %N A3067 PROBLIMES. %R A3067 AMM 80 677 73. %I A3068 N0389.8 %S A3068 1,2,4,7,11,15,19,23,28,33,38,43,48,53,58,63,68,73,79,85,91,97 %N A3068 PROBLIMES. %R A3068 AMM 80 677 73. %I A3403 N0392.3 %S A3403 1,2,4,7,11,18,27,41,60,87,122,172,235,320,430,572,751,982,1268, %T A3403 1629,2074,2625,3297,4123,5118,6324,7771,9506,11567,14023,16917,20335 %N A3403 CERTAIN TRIANGULAR ARRAYS OF INTEGERS. %R A3403 LMS13 118. %I A3292 N0392.5 %S A3292 1,2,4,7,11,19,29,46,70,106,156,232,334,482,686,971,1357,1894,2612, %T A3292 3592,4900,6656,8980,12077,16137,21490,28476,37600,49422,64763,84511 %N A3292 4-LINE PARTITIONS, DECREASING ACROSS ROWS. %R A3292 MTAC 26 1004 72. %I A3318 N0394.5 %S A3318 1,2,4,7,12,18,28,39,55,74,100,127,167,208,261,322,399,477,581,686, %T A3318 820,967,1142,1318,1545,1778,2053,2347,2697,3048,3486,3925,4441,4986,5610 %N A3318 A(N+1) = 1+A([N/1])+A([N/2])+...+A([N/N]). %R A3318 MR 38 384(2049) 69. RE3. %I A3293 N0397.5 %S A3293 1,2,4,7,12,21,34,56,90,143,223,348,532,811,1224,1834,2725,4031, %T A3293 5914,8638,12540,18116,26035,37262,53070,75292,106377,149738,209980 %N A3293 PLANAR PARTITIONS, DECREASING ACROSS ROWS. %R A3293 MTAC 26 1004 72. %C N0399 N0399 %S N0399 1,2,4,7,12,22,39,70,126,225,404,725,1299,2331,4182,7501,13458, %T N0399 24145,43316,77715,139430,250152,448808,805222,1444677,2591958,4650342 %N N0399 RESTRICTED PARTITIONS. %R N0399 EMS 11 224 59. 集成电路21、481、72、I、A316、N0403.5、S、A31 16、1、2、4、7、13、23、41、7212822688、6961179205、5569620310108、0 %T A31 16 1872135659580917175165959585958590084151590726881554π%N A31 16的一个行列式倒数的扩展。HPR. %I A2989 N0410.5 %S A2989 1,2,4,7,14,28,61,131,297,678,1592,3770,9096,22121,54451,135021, %T A2989 337651,849698,2152048,5479408,14022947,36048514,93061268,241160180 %N A2989 TREES WITH A FORBIDDEN LIMB. %R A2989 HA7 297. %I A2956 N0411.5 %S A2956 1,2,4,7,15,20,48,65,119,166 %N A2956 BASIC INVARIANTS FOR CYCLIC GROUP. %R A2956 IOWA 55 290 48. %I A3485 N0414.5 %S A3485 1,2,4,8,9,10,12,16,17,18,20,24,25,26,28,32,33,34,36,40,41,42,44,48, %T A3485 49,50,52,56,57,58,60,64,65,66,68,72,73,74,76,80,81,82,84,88,89,90,92,96 %N A3485 HURWITZ-RADON FUNCTION. %R A3485 LAM 131. %C A1148 N0416 %N A1148 A SELF-GENERATING SEQUENCE. %R A1148 PCPS 21 654 23. AMM 75 80 68.AND1. %I A2954 N0418.5 %S A2954 1,2,4,8,15,12,27,24,36,90,96,245,288,368,676,1088,2300,1596,1458, %T A2954 3344,3888,5360,8895,11852,25971,23360,38895,35540,35595,36032,53823 %N A2954 RELATED TO CHOWLA'S FUNCTION. %R A2954 MTAC 25 924 71. %I A3241 N0419.5 %S A3241 1,2,4,8,15,26,45,71,110,168,247 %N A3241 ACHIRAL ROOTED TREES. %R A3241 HA10. %C N0420 N0420 %N N0420 STACKS, OR PLANAR PARTITIONS. %R N0420 PCPS 47 686 51. QJMO 23 153 72. %I A3240 N0429.5 %S A3240 1,2,4,8,16,31,62,120,236,454,904 %N A3240 PARTIALLY ACHIRAL ROOTED TREES. %R A3240 HA10. %I A3427 N0432.5 %S A3427 1,2,4,8,16,34,72,158,348,784,1777,4080,9425,21965,51456,121300, %T A3427 287215,683268,1631532,3910235,9401000,22670058,54813780,132867903 %N A3427 TREES BY STABILITY INDEX. %R A3427 CM2 50. %I A2955 N0435.5 %S A2955 1,2,4,8,17,36,79,175,395,899,2074 %N A2955 TRIMMED TREES. %R A2955 AMM 80 874 73. %I A3426 N0435.6 %S A3426 1,2,4,8,17,37,85,196,469,1134,2799,6975,17628,44903,115497,299089, %T A3426 780036,2045924,5396078,14299878,38067356,101748748,272995157,735004112 %N A3426 STABLE TREES. %R A3426 CM2 50. %I A3007 N0435.8 %S A3007 1,2,4,8,17,38,89,208 %N A3007 N-LEVEL EXPRESSIONS. %R A3007 AMM 80 876 73. %I A3008 N0436.5 %S A3008 1,2,4,8,17,39,90,213 %N A3008 N-LEVEL EXPRESSIONS. %R A3008 AMM 80 876 73. %I A3081 N0438.5 %S A3081 1,2,4,8,19,48,126 %N A3081 TRIANGULAR CACTI. %R A3081 HA8 73. %I A3018 N0453.3 %S A3018 1,2,4,9,20,47,111,270,664,1659 %N A3018 N-LEVEL EXPRESSIONS. %R A3018 AMM 80 874 73. %I A3019 N0453.6 %S A3019 1,2,4,9,20,48,114,282,703,1787 %N A3019 N-LEVEL EXPRESSIONS. %R A3019 AMM 80 874 73. %I A3320 N0462.5 %S A3320 1,2,4,9,27,81,256,1024,4096,16384,78125,390625,1953125,10077696, %T A3320 60466176,362797056,2176782336,13841287201,96889010407,678223072849 %N A3320 A(N) = MAX OF K**(N-K). %R A3320 TO1 231. %I A3407 N0462.8 %S A3407 1,2,4,10,20,48,104,282,496,1066,2460,6128,12840,29380,74904,212728, %T A3407 368016,659296,1371056,2937136 %N A3407 PERMUTATIONS WITH NO 3-TERM ARITHMETIC PROGRESSION. %R A3407 JLMS 11 263 36. AMM 82 76 75. %I A3104 N0466.5 %S A3104 1,2,4,10,24,67 %N A3104 HEXAGONAL POLYOMINOES WHOSE GRAPH IS A PATH. %R A3104 GTA 216. %I A3239 N0469.5 %S A3239 1,2,4,10,26,80,246,810,2704,9252,32066 %N A3239 ROOTED PLANE TREES. %R A3239 HA10. %I A3223 N0470.5 %S A3223 1,2,4,10,28,130 %N A3223 SUPERPOSITIONS OF CYCLES. %R A3223 AM1 131 143 73. %I A3289 N0471.5 %S A3289 1,2,4,10,30,98,328,1140,4040,14542,53060,195624,727790,2728450, %T A3289 10296720 %N A3289 WALKS ON A TRIANGULAR LATTICE. %R A3289 PHYSA 6 352 73. %I A3422 N0472.5 %S A3422 1,2,4,10,34,154,874,5914,46234,409114,4037914,43954714,522956314, %T A3422 6749977114,93928268314,1401602636314,22324392524314,378011820620314 %N A3422 SUM OF FACTORIAL(N). %R A3422 BALK 1 147 71. MR 44 733(3945)72 .0 %C N047 3 N047 3 S 1 0 2 0 4 3 1,2 2 4,10,36202 1828 338 699200 4 3025 1722 23 205 18948 316359580362,% T N047 3 77477180493604 %N N047 3改变货币-与二元分配函数有关。NMT 10 65,62。PCPS 66 376,69。At1 400 .%%C N047 7N047 7 %N N047 7置换群,%R R N047 7 JPC 33 1069 29。JL2 169. %C N0478 N0478 %S N0478 1,2,4,11,33,116,435,1832,8167,39700,201785,1099449,6237505,37406458 %N N0478 REFINEMENTS OF PARTITIONS. %R N0478 GU5. %I A3222 N0482.5 %S A3222 1,2,4,12,39,208 %N A3222 SUPERPOSITIONS OF CYCLES. %R A3222 AM1 131 143 73. %C N0484 N0484 %S N0484 1,2,4,12,56,456,6880,191536,9733056,903753248,154108311168, %T N0484 48542114686912,28401423719122304,31021002160355166848 %N N0484 TOURNAMENTS. %R N0484 MO1 87. HA8 245. %I A3180 N0484.5 %S A3180 1,2,4,12,80,3984,37333248 %N A3180 BOOLEAN FUNCTIONS. %R A3180 MU4 38. %Q N0485 N0485 %R N0485 MU4 38. %I A3500 N0490.5 %S A3500 1,2,4,14,52,194,724,2702,10084,37634,140452,524174,1956244,7300802, %T A3500 27246964,101687054,379501252,1416317954,5285770564,19726764302 %N A3500 A(N) = 4A(N-1) - A(N-2). %R A3500 JSH1. %I A3322 N0491.5 %S A3322 1,2,4,14,62 %N A3322 NECKLACE PERMUTATIONS. %R A3322 AMM 81 340 74. %Q N0492 N0492 %R N0492 MU4 38. %Q N0494 N0494 %R N0494 MU4 38. %I A3514 N0494.3 %S A3514 1,2,4,15,102,4166,402631,76374899,27231987762,18177070202320, %T A3514 22801993267433275,54212469444212172845,246812697326518127351384 %N A3514 SERIES-REDUCED GRAPHS. %R A3514 JRE1. %I A3433 N0494.5 %S A3433 1,2,4,16,48,160,576,4096,14336,73728,327680,2985984,14929920, %T A3433 77635584 %N A3433 LARGEST DETERMINANT OF (+1,-1)-MATRIX. %R A3433 ZAMM 42 T21 62. MZT 83 12764。AMM 79 626 72. %I A3256 N0508.2 %S A3256 1,2,5,7,9,12,14,17,19,21,24,26,28,31,33,36,38,40,43,45,47,49,51,54, %T A3256 56,58,61,63,66,68,70 %N A3256 RELATED TO FIBONACCI REPRESENTATIONS. %R A3256 FQ 11 385 73. %I A3153 N0508.5 %S A3153 1,2,5,7,10,12,14,17,19,22,24,26,29,31,34,36,39,41,43,46,48 %N A3153 RELATED TO PELLIAN REPRESENTATIONS OF NUMBERS. %R A3153 FQ 10 487 72. %Q N0509 N0509 %R N0509 FQ 11 385 73. %I A3314 N0515.2 %S A3314 1,2,5,8,12,16,20,24,29,34,39,44,49,54,59,64,70,76,82,88,94,100,106, %T A3314 112,118,124,130,136,142,148,154,160,167,174,181,188,195,202,209,216,223 %N A3314 A(N) = N + MIN(A(K)+A(N-K)). %R A3314 KN1 3 374. %I A2960 N0515.5 %S A2960 1,2,5,8,12,17,22,28,34,41,48,56,65,74,84,94,105,116,128,140,153, %T A2960 166,180,194,209,224,240,257,274,292,310,329,348,368,388,409,430,452,474 %N A2960 THE SQUARE SIEVE. %R A2960 JRM 4 288 71. %I A3058 N0526.5 %S A3058 1,2,5,9,19,34,69,125,251,462,925,1729,3459,6554,13109,25125,50251, %T A3058 97222,194445,379049,758099,1486674,2973349,5858125,11716251,23166782 %N A3058 POPULATION OF MULTIPLES OF 3 WITH EVEN NUMBER OF 1-BITS. %R A3058 PC1 1 4-973. %I A3192 N0531.5 %S A3192 1,2,5,10,17,24,35 %N A3192 MAXIMAL UNCROSSED KNIGHT'S PATH ON CHESSBOARD. %R A3192 JRM 2 157 69. %I A3420 N0541.5 %S A3420 1,2,5,11,14,26,41,89,101,194,314,341,689,1091,1154,1889,2141,3449, %T A3420 3506,5561,6254,8126,8774,10709,13166,15461,24569 %N A3420 EXTREME VALUES OF DIRICHLET SERIES. %R A3420 PSPM 24 278 73. %I A3416 N0551.5 %S A3416 1,2,5,12,28,64,144,320,704,1536,3328,7168,15360,32768,69632,147456, %T A3416 311296,655360,1376256,2883584,6029312,12582912,26214400,54525952 %N A3416 (N+5)2**N. %R A3416 %I A3089 N0554.5 %S A3089 1,2,5,12,30,79,227,710,2322,8071,29503,112822,450141 %N A3089 CONNECTED LINE GRAPHS. %R A3089 HA8 221. %C N0558 N0558 %S N0558 1,2,5,12,33,90,261,766,2312,7068,21965,68954,218751,699534,2253676, %T N0558 7305788,23816743,78023602,256738751,848152864,2811996972,9353366564 %N N0558 SER减少了种植树木。%%R N055 8 Cayy 3 246。RI1Me2.0%N057 2.0%S.A3080,1,2,5,13,37 111345,10%N,A3080根部三角形仙人掌。%%A1011 N057 6 %S S A1011,1,2,5,14,38,120,358352,162,22666,12162,230895601301140,%的T A1011 4215748 4215748 %N A1011折叠一条邮票。%%R A1011山姆209(3)262 63。JCT 5 151 151 .0%C N0581N0581%S S N0581,1,2,5,14,51267,3656%,N N0581-阶群2,4,8,16,…,128。% %R N0581HS1。ERR. %I A3430 N0582.5 %S A3430 1,2,5,15,48,167 %N A3430 POSETS GENERATED BY UNIONS AND SUMS. %R A3430 PAMS 45 298 74. %Q N0588 N0588 %R N0588 PL2 4 180 73. %I A3149 N0588.5 %S A3149 1,2,5,16,64,312,1812,12288,95616,840960,8254080,89441280, %T A3149 1060369920,13649610240,189550368000,2824077312000,44927447040000 %N A3149 SUM OF FACTORIAL(K).FACTORIAL(N-K). %R A3149 HWG. %Q N0592 N0592 %R N0592 OG1 116. %I A3456 N0593.5 %S A3456 1,2,5,17,62,275,1272,6225,31075,158376,816229,4251412,23319056, %T A3456 117998524,627573216,3355499036,18025442261,97239773408,526560862829 %N A3456 DISSECTIONS OF A POLYGON. %R A3456 REA1. %I A3510 N0593.7 %S A3510 1,2,5,17,67,352,1969,13295,97619,848354,7647499,82862683,897904165, %T A3510 11226063188,146116260203,2089038231953,30230018309161,508450431515290 %N A3510 AN EQUIVALENCE RELATION ON PERMUTATIONS. %R A3510 AMM 82 87 75. %Q N0594 N0594 %R N0594 AMM 79 519 72. %I A3069 N0597.5 %S A3069 1,2,5,20,88,632,8816 %N A3069 DIGRAPHS WITH SAME CONVERSE AS COMPLEMENT. %R A3069 HA7 200. %I A3163 N0598.5 %S A3163 1,2,5,20,350,140,1050,300,57750,38500,250250,45500,2388750,367500, %T A3163 318750,42500,1088106250,128012500,960093750,101062500,105761906250 %N A3163 DENOMINATORS OF VAN DER POL NUMBERS. %R A3163 JRAM 260 35 73. %I A3501 N0601.5 %S A3501 1,2,5,23,110,527,2525,12098,57965,277727,1330670,6375623,30547445, %T A3501 146361602,701260565,3359941223,16098445550,77132286527,369562987085 %N A3501 A(N) = 5A(N-1) - A(N-2). %R A3501 JSH1. %I A3095 N0602.5 %S A3095 1,2,5,26,677,458330,210066388901,44127887745906175987802, %T A3095 1947270476915296449559703445493848930452791205 %N A3095 A(N) = A(N-1)**2 + 1. %R A3095 FQ 11 429 73. %C N0603 N0603 %S N0603 1,2,5,27,923,909182,1046593950039,1168971346319460027570137, %T N0603 1730152138254248421873938035305987364739567671241 %N N0603 CONVERGENTS TO LEHMER'S CONSTANT. %R N0603 DMJ 4 334 38. JWW.0%6N0606 N0606,S N0606,1,2,5,34 21313848,1788 768,266565,33045,25811616897504,%N 0606与3个参数的关系。HA8 231。DM 6 384 73. %I A3145 N0613.5 %S A3145 1,2,6,9,13,15,19,22,26,30,33,37,39,43,46,50,53,57,59,63,66,70,74, %T A3145 77,81,83,87,90,94,96,100,103,107,111,114,118,120,124,127,131,134,138 %N A3145 A SELF-GENERATING SEQUENCE. %R A3145 FQ 10 49 72. %I A3274 N0616.5 %S A3274 1,2,6,12,20,34,56,88,136,208,314,470,700,1038,1534,2262,3330,4896, %T A3274 7192,10558,15492,22724,33324,48860,71630,105002,153912,225594,330650 %N A3274 KEY PERMUTATIONS. %R A3274 CJ1 14 152 71. %I A3418 N0619.5 %S A3418 1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,360360, %T A3418 720720,12252240,12252240,232792560,232792560,232792560,232792560 %N A3418 LCM(1,2,...,N). %R A3418 AND2. %C A2319 N0621 %S A2319 1,2,6,12,60,168,360,660 %N A2319 LARGEST GROUP WITH N CONJUGACY CLASSES. %R A2319 CJM 20 457 68. 形式:% %R R A3039 DA3 18 3 71.CRV 13 415 72。A1.21%I A3039 N0622.5%S A3039,1,2,6,13,32,92 %,N A3039在析取范式中的最大项数BR1 17 .I.A3268N0623.8S.A3268,A3268,1,2,6,15,6026018201136613615141451326261234 48 8605194,% %T A3268 141695662641151508606196048 19307070908611719420910%%A3268中心纤维系数,% R R A3268 FQ 6 82 82。BR1 74 .i %A3142 N06285.5%S A3142,1,2,6,16,43,%N 3A3142最大的3x3X子集…CUBE WITH NO 3 POINTS COLLINEAR. %R A3142 DM 4326 73. %I A3291 N0628.8 %S A3291 1,2,6,16,46,140,464,1580,5538,19804,71884,264204,980778,3671652, %T A3291 13843808 %N A3291 WALKS ON A TRIANGULAR LATTICE. %R A3291 PHYSA 6 352 73. %I A3446 N0631.5 %S A3446 1,2,6,16,52,170,579,1996,7021,24892,89214,321994,1170282 %N A3446 DISSECTIONS OF A POLYGON. %R A3446 REA1. %C N0645 N0645 %S N0645 1,2,6,20,76,312,1384,6512,32400,168992,921184,5222208,30710464, %T N0645 186753920,1171979904,7573069568,50305536256,342949298688,2396286830080 %N N0645 A(N) = 2(A(N-1) + (N-1)A(N-2)). %R N0645 LU1 1 221. (i)A309N064,5%S,A30941,66/20105,n%a309-连通平面图。% %R A3094WI1 162。π%N064 8 N064 8 %,R N064 8 PL2 4 4 180。RI1ST1。JCT 9 352 352。PL2 4 265 73. %I A3450 N0658.5 %S A3450 1,2,6,24,89,371,1478,6044,24302,98000,392528,1570490 %N A3450 DISSECTIONS OF A POLYGON. %R A3450 REA1. %I A3454 N0659.5 %S A3454 1,2,6,25,107,509,2468,12258,61797,315830,1630770,8498303,44629855, %T A3454 235974495,1255105304,6710883952,36050676617,194478962422,1053120661726 %N A3454 DISSECTIONS OF A POLYGON. %R A3454 REA1. %C N0664 N0664 %S N0664 1,2,6,26,166,1626,25510,664666,29559718,2290267226,314039061414, %T N0664 77160820913242 %N N0664 FROM THE BINARY PARTITION FUNCTION. %R N0664 PRSE 65 190 59. PCPS 66 376 69.AT1 400. %I A3513 N0664.5 %S A3513 1,2,6,27,192,2280 %N A3513 IRREDUNDANT WEIGHTED BINARY CODES. %R A3513 DA5. %I A3266 N0668.5 %S A3266 1,2,6,30,240,3120,65520,2227680,122522400,10904493600, %T A3266 1570247078400,365867569267200,137932073613734400,84138564904377984000 %N A3266 PRODUCTS OF FIBONACCI NUMBERS. %R A3266 BR1 69. %I A3087 N0669.5 %S A3087 1,2,6,31,302,5984 %N A3087 ACYCLIC DIGRAPHS. %R A3087 HA8 194. %I A3499 N0670.5 %S A3499 1,2,6,34,198,1154,6726,39202,228486,1331714,7761798,45239074, %T A3499 263672646,1536796802,8957108166,52205852194,304278004998,1773462177794 %N A3499 A(N) = 6A(N-1) - A(N-2). %R A3499 BE3 198. JSH1. %I A3053 N0679.5 %S A3053 1,2,6,48,720,23040,1451520,185794560,47377612800,24257337753600, %T A3053 24815256521932800,50821645356918374400,208114637736580743168000 %N A3053 ORDER OF ORTHOGONAL GROUP OVER GF(2). %R A3053 AMM 76 158 69. %I A3189 N0683.5 %S A3189 1,2,6,156,7013488,29288387523484992, %T A3189 234431745534048922731115019069056 %N A3189 3-PLEXES. %R A3189 DM 6 384 73. %I A3061 N0684.5 %S A3061 1,2,7,7,11,15 %N A3061 NONABELIAN GROUPS WITH N CONJUGACY CLASSES. %R A3061 CJM 20 457 68. 1.1.0%C N0685 N0685·%N N0685置换群。%R N0685 JPC 33 1069 1069。JL2 169,I,A3158,N068,5,S,A3158,A3158,1,2,7,10,13,18,23,39,42,45,50,53,6,1,6,1,76,77,77,8,2,8,T A3158,92,95995,98101131161191641127113514114141156151156159,%N A3158的自生序列,% R R A3158 FQ 10 500 500。BR1 67. %I A3452 N0690.5 %S A3452 1,2,7,15,28,45,69,98,136,180,235,297,373 %N A3452 DISSECTIONS OF A POLYGON. %R A3452 REA1. %I A3480 N0699.3 %S A3480 1,2,7,24,82,280,956,3264,11144,38048,129904,443520,1514272,5170048, %T A3480 17651648,60266496,205762688,702517760,2398545664,8189147136,27959497216 %N A3480 A(N) = 4A(N-1) - 2A(N-2). %R A3480 MTAC 29 220 75. %I A3041 N0699.5 %S A3041 1,2,7,24,92,388 %N A3041 VACUOUSLY TRANSITIVE RELATIONS. %R A3041 DM 4 194 73. %I A3447 N0701.5 %S A3447 1,2,7,26,108,434,1765,7086,28384,113092,449582,1783092,7062611 %N A3447 DISSECTIONS OF A POLYGON. %R A3447 REA1. %I A3437 N0703.5 %S A3437 1,2,7,29,196,1788,21994 %N A3437 HAMILTONIAN CIRCUITS ON N-OCTAHEDRON. %R A3437 SI4. %I A3059 N0725.5 %S A3059 1,2,8,16,45,90,220,440,1001,2002,4368,8736,18565,37130,77540, %T A3059 155080,320001,640002,1309528,2619056,5326685,10653370,21572460,43144920 %N A3059 POPULATION OF MULTIPLES OF 3 WITH ODD NUMBER OF 1-BITS. %R A3059 PC1 1 4-973. %C N0730 N0Nd730、N2730、1,2、8、26、80268944、42472492467、1912727、445、2429、24680、πT N0730 1159628446364456 1159628446364456 %N N0730金刚石点阵磁化,%R N0730 JMP 6 6 297 65。PHYSA 6 1511 73. %I A3175 N0731.5 %S A3175 1,2,8,31,139,724 %N A3175 CUBIC GRAPHS. %R A3175 MO4. %I A3304 N0731.8 %S A3304 1,2,8,32,144,708,3696,20296 %N A3304 FIGURE 8'S ON THE SQUARE LATTICE. %R A3304 PHYSA 3 23 70. %I A3445 N0736.2 %S A3445 1,2,8,40,165,712,2912,11976,48450,195580,784504,3139396 %N A3445 DISSECTIONS OF A POLYGON. %R A3445 REA1. %I A3305 N0736.5 %S A3305 1,2,8,40,208,1120,6200,35236 %N A3305 FIGURE 8'S ON THE SQUARE LATTICE. %R A3305 PHYSA 3 24 70. %C N0737 N0737 %S N0737 1,2,8,40,240,1680,13440,120960,1209600,13305600,159667200, %T N0737 2075673600,29059430400,435891456000,6974263296000,118562476032000 %N N0737 FACTORIAL(N)/3. %R N0737 TOH 42 152 36. %I A3091 N0741.3 %S A3091 1,2,8,45,416,6657,189372,9695869,902597327,154043277297, %T A3091 48535481831642,28400190511772276,31020581422991798557 %N A3091 [(2**C(N,2))/FACTORIAL N]. %R A3091 HA8 246. %I A3275 N0741.5 %S A3275 1,2,8,48,80,96,128,240,288,480,1008,1200,1296,1440,1728,2592,2592, %T A32758000 5600、408086401、4040124、1497、1900、1900、1900、192、242、242、247、57、6、n、A3255值φ(n)=φ(n+1)。MI2. %I A3032 N0741.8 %S A3032 1,2,8,48,98,350,440,2430,2430,13310,13454,17575,212380 %N A3032 EVERY SEQ OF 3 NUMBERS > A(N) CONTAINS A PRIME > P(N). %R A3032 AMM 79 108772. %I A3301 N0752.5 %S A3301 1,2,8,496,9088,12032,12004352,4139008,51347456 %N A3301 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3301 RS3 273 593 73. %I A3125 N0762.5 %S A3125 1,2,9,36,142,558,2189,8594,33796 %N A3125 VALUE OF AN URN. %R A3125 DM 5 307 73. %I A3161 N0762.8 %S A3161 1,2,9,36,190,980,5705,33040,204876,1268568,8209278,53105976, %T A3161 354331692,2364239592,16140234825,110206067400 %N A3161 A BINOMIAL COEFFICIENT SUMMATION. %R A3161 AMM 81 170 74. %C A2825 N0765 %N A2825 PRECOMPLETE POST FUNCTIONS. %R A2825 SMD 10 619 69. JCT14A 6 73 .0%C0A0170N775,S A0170,1,2,10,4,40,923 5242680801407737,12123696227 91841477 2512%%N A0170昆斯问题。% %R A0170 PSAM 10 10 93 60。WE2 238。LI2。RE5. %I A3093 N0783.5 %S A3093 1,2,10,83,690,6412,61842,457025 %N A3093 PLANAR 2-TREES. %R A3093 JLMS 6 592 73. %I A3046 N0784.5 %S A3046 1,2,10,140,5880,776160,332972640,476150875200,2315045555222400, %T A3046 38883505145515430400,2285805733484270091494400 %N A3046 FACTORIAL CATALAN NUMBERS. %R A3046 MO3. %Q N0785 N0785 %R N0785 MU4 38. %I A3047 N0785.5 %S A3047 1,2,10,280,235200,173859840000,98238542885683200000000, %T A3047 32169371027674057560745102540800000000000000000 %N A3047 DOUBLE FACTORIAL CATALAN NUMBERS. %R A3047 MO3. %C N0788 N0788 %N N0788 THE NO-THREE-IN-LINE PROBLEM. %R N0788 GU3. WE1 124。CM2 7. %I A3442 N0791.5 %S A3442 1,2,11,48,208,858,3507,14144,56698,226100,898942,3565920,14124496 %N A3442 DISSECTIONS OF A POLYGON. %R A3442 REA1. %I A3167 N0793.5 %S A3167 1,2,11,101,102,202,211,1001,1021,2002,10001,10022,11012,12201, %T A3167 20002,100001,100201,200002,201102,1000001,1000222,1002201,1011221 %N A3167 BASE 3 NUMBERS WHOSE SQUARE IS A PALINDROME. %R A3167 JRM 5 15 72. %I A3088 N0794.5 %S A3088 1,2,11,172,8603 %N A3088 UNILATERAL DIGRAPHS. %R A3088 HA8 218. %I A3493 N0799.3 %S A3493 1,2,12,50,180,606,1924,5910,17564,51186,146180 %N A3493 SUSCEPTIBILITY FOR SQUARE LATTICE. %R A3493 DG2 136. %I A3123 N0807.5 %S A3123 1,2,12,92,800,7554,75664,792448,8595120,95895816,1095130728, %T A3123 12753454896 %N A3123 HAMILTONIAN ROOTED TRIANGULATIONS. %R A3123 DM 6 167 73. %C N0808 N0808 %N N0808 1.3.5...(2N-1).2**N. %R N0808 MTAC 3 168 48. %Q N0809 N0809 %R N0809 PL2 4 180 73. %I A3121 N0810.5 %S A3121 1,2,12,286,33592,23178480,108995910720 %N A3121 STRICT S投票号码:N个候选人,第i个候选人得到我的选票。AMS 36 241 241。MA3%C8A6060N0812%S A2660,1,2,1257,16128081285,1200,679490,1990,400,10877,608324590829 56800,% %T A28 60 55 2475 14961568928 42531225600 600 %N A28 60拉丁方。RYS 53。JCT 3 98 98。DM 11 94 75. %I A3042 N0812.5 %S A3042 1,2,12,2688,1813091520 %N A3042 HAMILTONIAN CYCLES ON A CUBE. %R A3042 SAM 228 (4) 111 73. %I A3507 N0816.3 %S A3507 1,2,13,199,3773 %N A3507 RIGID TOURNAMENTS. %R A3507 DM 11 65 75. %I A3085 N0816.5 %S A3085 1,2,13,199,9364,1530843,880471142,1792473955306 %N A3085 CONNECTED DIGRAPHS. %R A3085 HA8 124. %I A3025 N0823.5 %S A3025 1,2,15,316,16885,2174586,654313415,450179768312,696979588034313, %T A3025 2398044825254021110 %N A3025 ACYCLIC DIGRAPHS WITH 1 OUT-POINT. %R A3025 HA7 254. %I A3419 N0832.5 %S A3419 1,2,17,167,227,362,398 %N A3419 EXTREME VALUES OF DIRICHLET SERIES. %R A3419 PSPM 24 277 73. %I A3043 N0834.5 %S A3043 1,2,18,5712,5859364320 %N A3043 HAMILTONIAN PATHS ON A CUBE. %R A3043 SAM 228 (4) 111 73. %I A3283 N0834.8 %S A3283 1,2,20,70,112,352,1232,22880,183040 %N A3283 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3283 RS3 273 590 73. %I A3490 N0837.3 %S A3490 1,2,20,142,880,5106,28252,152142,799736,4141426,21133476,106827054 %N A3490 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3490 DG2 136. %I A3481 N0837.7 %S A3481 1,2,20,143,986,6764,46367,317810,2178308,14930351,102334154, %T A3481 701408732,4807526975,32951280098,225851433716,1548008755919 %N A3481 A(N) = 7A(N-1) - A(N-2) + 5. %R A3481 DM 9 89 74. %I A3102 N0850.5 %S A3102 1,2,24,420,27720,720720,36756720,5354228880,481880599200, %T A3102 72201776446800,10685862914126400 %N A3102 LARGEST NUMBER DIVISIBLE BY ALL NUMBERS < ITS N-TH ROOT. %R A3102 CH2 3 42962. 30先生213(1085)65。PME 4 124 65. %I A3092 N0860.5 %S A3092 1,2,36,1200,57000,3477600,257826240,22438563840,2238543216000, %T A3092 251584613280000,31431367287936000,4319334744012288000 %N A3092 LABELED PLANAR 2-TREES. %R A3092 JLMS 6 590 73. %C A2542 N0869 %S A2542 1,2,56,16256,1073709056,4611686016279904256, %T A2542 85070591730234615856620279821087277056 %N A2542 COMPLETE POST FUNCTIONS. %R A2542 PLMS 16 191 66. %I A2945 N0880.5 %S A2945 1,3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,2,1,3,4,1,1,2,14,3,12,1, %T A2945 15,3,1,4,534,1,1,5,1,1,121,1,2,2,4,10,3,2,2,41,1,1,1,3,7,2,2,9,4,1,3,7 %N A2945 CONTINUED FRACTION EXPANSION OF CUBE ROOT OF 2. %R A2945 JRAM 255 118 72. %I A2972 N0880.8 %S A2972 1,3,1,5,1,5,7,5,3,5,9,1,3,7,11,7,11,13,9,7,1,15,13,15,1,13,9,5,17, %T A2972 13,11,9,5,17,7,17,19,1,3,15,17,7,21,19,5,11,21,19,13,1,23,5,17,19,25,13 %N A2972 QUADRATIC PARTITIONS OF PRIMES. %R A2972 KK1 243. %C N0883 N0883 %N N0883 A(N) = -A(N-1) - 2A(N-2). %R N0883 JA2 82. AMM 79 772 72. %I A3188 N0891.5 %S A3188 1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,28,20,21, %T A3188 23,22,18,19,17,16,48,49,51,50,54,55,53,52,60,61,63,62,58,59,57,56,40,41 %N A3188 DECIMAL EQUIVALENTS OF REFLECTED GRAY CODE FOR THE INTEGERS. %R A3188 SAM 227 (2) 107 72. %I A3034 N0899.5 %S A3034 1,3,3,4,3,3,4,6,5,6,6,6,7 %N A3034 MINIMUM NUMBER OF ORDINARY LINES. %R A3034 MMAG 41 34 68. GR3 18. %C N0909 N0909 %N N0909 A SELF-GENERATING SEQUENCE. %R N0909 UL1 IX. JCT 12A 39 72. %I A3310 N0909.3 %S A3310 1,3,4,5,7,8,11,13,17,19,20,26,29,32,37,38,43,49,50,56,62,67,68,71, %T A3310 73,86,89,91,98,103,113,116,121,127,131,133,137,140,151,158,161,169,173 %N A3310 GENERATED BY A SIEVE. %R A3310 PC1 2 13-6 74. %I A3159 N0909.5 %S A3159 1,3,4,5,7,9,11,12,13,15,16,17,19,20,21,23,25,27,28,29,31,33,35,36, %T A3159 37,39,41,43,44,45,47,48,49,51,52,53,55,57,59,60,61,63,64,65,67,68,69,71 %N A3159 A SELF-GENERATING SEQUENCE. %R A3159 FQ 10 501 72. %I A3312 N0910.5 %S A3312 1,3,4,5,7,10,14,20,29,43,64,95,142,212,317,475,712,1067,1600,2399, %T A3312 3598,5396,8093,12139,18208,27311,40966,61448,92171,138256,207383,311074 %N A3312 GENERATED BY A SIEVE. %R A3312 PC1 2 17-16 74. %Q N0917 N0917 %R N0917 FQ 11 385 73. %I A3257 N0919.5 %S A3257 1,3,4,6,8,10,11,13,15,16,18,20,22,23,25,27,29,30,32,34,35,37,39,41, %T A3257 42,44,46,48,50,52,53,55,57,59,60,62,64,65,67,69 %N A3257 RELAT11、385、32.1、3、4、7、8、11、12、15、16、19、20、24、27、32、35、36、40、43、48、51、52、60、64、1、T、A3171、67、72、75、84、88、91、96、99、1001、121、151、112、152、142、142、148、163、163、168、180、0、n、A3171虚数二次域(有限序列)。Fibonacci表示。Bo1 426 .0%C A0925 N0922%N A0925虚数二次场(有限序列)。%R A0925 DI3 85。Bo1 426 .0%I A3141 N0922.3%S S A3141,1,3,4,7,8,12,15,20%%N A3141最大弧数最少,其反转产生传递性竞赛。%R A3141 MSH 37 23 23。MR 46 15(87) 73. %I A2977 N0922.5 %S A2977 1,3,4,7,9,10,13,15,19,21,22,27,28,31,39,40,43,45,46,55,57,58,63,64, %T A2977 67,79,81,82,85,87,91,93,94,111,115,117,118,121,127,129,130,135,136,139 %N A2977 IF A IS IN THE SEQUENCE SO ARE 2A+1 AND 3A+1. %R A2977 NAMS 18 960 71. %I A3136 N0922.8 %S A3136 1,3,4,7,9,12,13,16,19,21,25,27,28,31,36,37,39,43,48,49,52,57,61,63, %T A3136 64,67,73,75,76,79,81,84,91,93,97,100,103,108,109,111,112,117,121,124,127 %N A3136 CONTAIN PRIMES 3N+2 TO EVEN POWER. %R A3136 MMAG 55 377 71. %I A2986 N0942.5 %S A2986 1,3,4,12,27,84,247,826,2777,9868 %N A2986 HYDROCARBONS. %R A2986 GTA 257. %Q N0947 N0947 %R N0947 KR1 2 85. %Q N0948 N0948 %R N0948 KR1 2 85. %I A3152 N0949.5 %S A3152 1,3,5,6,8,10,11,13,15,17,18,20,22,23,25,27,29,30,32,34 %N A3152 A BEATTY SEQUENCE. %R A3152 FQ 10 487 72. %D A1838 N0951 %I A1838 N0953.1 %S A1838 1,3,5,6,11,12,14,17,18,20,29,41,44,59,62,71,92,101,107,116,137,149, %T A1838 164,179,191,197,212,227,239,254,269,281,311,332347356419431452461πn A1838φ(n+2)=φ(n)+2。% r r a1838 AMM 56 22 49。AS1 840. %I A3144 N0953.3 %S A3144 1,3,5,7,8,10,12,14,16,18,20,21,23,25,27,29,31,32,34,36,38,40,42,44, %T A3144 45,47,49,51,52,54,56,58,60,62,64,65,67,69,71,73,75,76,78,80,82,84,86,88 %N A3144 A SELF-GENERATING SEQUENCE. %R A3144 FQ 10 49 72. %I A3052 N0953.5 %S A3052 1,3,5,7,9,20,31,42,53,64,75,86,97,108,110,121,132,143,154,165,176, %T A3052 187,198,209,211,222,233,244,255,266,277,288,299,310,312,323,334,345,356 %N A3052 SELF OR COLOMBIAN NUMBERS. %R A3052 KA1. AMM 81 407 74. %I A3219 N0953.6 %S A3219 1,3,5,7,9,20,42,108,110,132,198,209,222,266,288,312,378,400,468, %T A3219 512,558,648,738,782,804,828,918,1032,1098,1122,1188,1212,1278,1300,1368 %N A3219 SELF NUMBERS WHICH ARE DIVISIBLE BY THE SUM OF THEIR DIGITS. %R A3219 KA2. %I A3070 N0953.8 %S A3070 1,3,5,7,10,13,16,19,22,26,29,33,37,41,45,49,53,57,62,66,70,75,80, %T A3070 84,89,94,98,103,108,113,118,123,128,133,139,144,149,154,160,165,170,176 %N A3070 SMALLEST INTEGER > LOG2( FACTORIAL N). %R A3070 KN1 3 187. %I A3255 N0954.5 %S A3255 1,3,5,7,11,13,16,18,20,22,26,28,30,32,36,38,41 %N A3255 RELATED TO FIBONACCI REPRESENTATIONS. %R A3255 FQ 11 385 73. %I A3424 N0956.3 %S A3424 1,3,5,7,13,17,31,73,127,257,307,757,1093,1723,2801,3541,5113,8011, %T A3424 8191,10303,17293,19531,28057,30103,30941,65537,86143,88741,131071,147073 %N A3424 PRIMES OF FORM (P**A - 1)/(P**B - 1), P=PRIME. %R A3424 IJM 6 154 62. %I A3229 N0956.5 %S A3229 1,3,5,7,13,23,37,63,109,183,309,527,893,1511,2565,4351,7373,12503, %T A3229 21205,35951,60957,103367,175269,297183,503917,854455,1448821,2456655 %N A3229 A(N) = A(N-1) + 2A(N-3). %R A3229 DA4. %I A2957 N0960.5 %S A2957 1,3,5,7,27,53,147,401 %N A2957 2.10**N - 1 IS PRIME. %R A2957 PL2 2 567 71. %I A3265 N0962.5 %S A3265 1,3,5,8,10,12,14,16,18,21,23,25,27,29,32,34,36,38,40,42,45,47,49, %T A3265 52,54,56,58,60,62,65,67,69,71,73,76,78,80,82,84,86,89,91,93,95,97,99 %N A3265 NOT REPRESENTABLE BY TRUNCATED TRIBONACCI SEQUENCE. %R A3265 BR1 65. %C N0963 N0963 %N N0963 SUM OF INTEGER ABOVE LOG2(N). %R N0963 AFI 32 519 68. KN1 3 184. %I A3311 N0963.5 %S A3311 1,3,5,8,11,15,18,23,27,32,38,42,47,53,57,63,71,75,78,90,93,98,105, %T A3311 113,117,123,132,137,140,147,161,165,168,176,183,188,197,206,212,215,227 %N A3311 GENERATED BY A SIEVE. %R A3311 PC1 2 13-6 74. %I A3071 N0970.5 %S A3071 1,3,5,9,11,14,17,25,27,30,33,38,41,45,49,65 %N A3071 COMPARISONS FOR SORTING BY LIST MERGING. %R A3071 KN1 3 184. %I A3075 N0971.5 %S A3075 1,3,5,9,12,16,19 %N A3075 MINIMUM COMPARATORS IN SORTING NETWORK FOR N THINGS. %R A3075 KN1 3 227. %I A3217 N0975.5 %S A3217 1,3,5,9,17,35,79,209 %N A3217 WEIGHTS OF THRESHOLD FUNCTIONS. %R A3217 MU4 268. %I A3055 N0978.5 %S A3055 1,3,5,10,19,39 %N A3055 CONNECTED PLANAR GRAPHS BY EDGES. %R A3055 GA2 80. %I A3187 N0979.3 %S A3187 1,3,5,10,27,119 %N A3187 POSITIVE THRESHOLD FUNCTIONS. %R A3187 MU4 214. %I A3186 N0979.5 %S A3186 1,3,5,10,30,198 %N A3186 POSITIVE PSEUDO-THRESHOLD FUNCTIONS. %R A3186 MU4 214. %I A3182 N0979.8 %S A3182 1,3,5,10,30,210,16353 %N A3182 BOOLIN函数。%%R A3182 MU4 38。πq N0983N0983%%R N0983FQ 10 499 499。GTA 255. %I A2962 N0988.5 %S A2962 1,3,5,15,19,58 %N A2962 SIMPLE IMPERFECT SQUARED SQUARES. %R A2962 BO4. %I A3112 N0992.5 %S A3112 1,3,5,105,81,6765,175747,30375,25219857,142901109,4548104883 %N A3112 PERMANENTS OF SCHUR'S MATRIX. %R A3112 JNT 5 48 73. %I A3458 N0994.5 %S A3458 1,3,6,7,7,23,62,143,44,159,46,47,174,2239,239,719,241,5849,2098, %T A3458 2099,43196,14871,19574,35423,193049,2105,36287,1119,284,240479,58782 %N A3458 ALL PRIME FACTORS OF C(A(N),N) EXCEED N. %R A3458 MTAC 28 647 74. %I A3252 N0995.5 %S A3252 1,3,6,9,12,15,18,21,23,26,29,32,35,38,41,44,47,50,53,56,59,61,64, %T A3252 67,70,73,76,79,81,83,86,89,92,95,98,101,104,107,110,113,116,119,121,124 %N A3252 RELATED TO FIBONACCI REPRESENTATIONS. %R A3252 FQ 11 386 73. %C N1001 N1001 %S N1001 1,3,6,10,13,17,20,23,27,30,34,37,40,44,47,51,54,58,61,64,68 %N N1001 A BEATTY SEQUENCE. %R N1001 CMB 2 188 59. FQ 10 487 72. %I A3022 N1003.5 %S A3022 1,3,6,11,17,25,34,44,55,72 %N A3022 LENGTH OF GOLOMB RULERS. %R A3022 SAM 226 (6) 116 72. %I A3453 N1004.5 %S A3453 1,3,6,11,17,26,36,50,65,85,106,133 %N A3453 DISSECTIONS OF A POLYGON. %R A3453 REA1. %I A3082 N1005.5 %S A3082 1,3,6,11,18,32,48,75,111,160 %N A3082 MULTIGRAPHS WITH 4 POINTS. %R A3082 HA8 88. %I A3204 N1011.5 %S A3204 1,3,6,12,24,33,60,99,156,276,438,597 %N A3204 CLUSTER SERIES FOR HONEYCOMB. %R A3204 PRV 133 A315 64. DG2 225 .%%C N1012 N1012 N %N1012蜂窝状的敏感性。%%R N1012 PHA 28 931 931。物理层5,635,72,β%C N1013,N1013,N%N1013在蜂窝上行走,%%R N1013 JMP 2 61 61。PHYSA 5 659 72. %I A3477 N1019.5 %S A3477 1,3,6,14,33,71,150,318,665,1375,2830,5798,11825,24039,48742,98606, %T A3477 199113,401455,808382,1626038,3267809,6562295,13169814,26416318,52962681 %N A3477 FROM FOLDING A STRIP OF PAPER. %R A3477 DA4. %C N1021 N1021 %S N1021 1,3,6,15,27,63,120,252,495,1023,2010,4095,8127,16365,32640,65535, %T N1021 130788,262143,523770,1048509,2096127,4194303,8386440,16777200,33550335 %N N1021 SUM OF A(D), D DIVIDES N, = 2**(N-1). %R N1021 FQ 2 251 64. %C A0220 N1022 %S A0220 1,3,6,15,29,67,139,310,667,1480,3244,7241,16104,36192,81435,184452, %T A0220 418870,955860,2187664,5025990,11580130,26765230,62027433,144133676 %N A0220 ASYMMETRIC TREES. %R A0220 HA5 232. AJS. %I A3162 N1025.5 %S A3162 1,3,6,19,49,163,472,1626,5034,17769,57474,206487,688881,2508195, %T A3162 8563020 %N A3162 A BINOMIAL COEFFICIENT SUMMATION. %R A3162 AMM 81 170 74. %I A3185 N1025.8 %S A3185 1,3,6,20,168,7581 %N A3185 POSITIVE BOOLEAN FUNCTIONS. %R A3185 MU4 214. %I A3098 N1031.5 %S A3098 1,3,6,55,66,171,595,666,3003,5995,8778,15051,66066,617716,828828, %T A3098 1269621,1680861,3544453,5073705,5676765,6295926,35133153,61477416 %N A3098 PALINDROMIC TRIANGULAR NUMBERS. %R A3098 JRM 6 146 73. %I A3118 N1031.8 %S A3118 1,3,7,1,2,2,1,2,4,56,1,14,2,1,1,3,5,6,2,1,1,2,1,1,8,1,2,2,1,5,1,4, %T A3118 1,1,3,3,1,1,3,7,4,1,10,1,2,1,8,2,4,1,1,9,2,2,2,1,2,1,1,1,92,1,26,4,31,1 %N A3118 CONTINUED FRACTION EXPANSION OF FIFTH ROOT OF 4. %R A3118 HPR. JSH·εQ N1035 N1035·%R R N1035OG1 99。PC1 2 13-7 74. %I A3057 N1035.3 %S A3057 1,3,7,9,19,25,27,55,73,97,129,171,231,313,327,649,703,871,1161, %T A3057 2223,2463,2919,3711,6171,10971,13255,17647,23529,26623,34239,35655,52527 %N A3057 RELATED TO THE N GOES TO N/2 (IF EVEN) OR 3N+1 (IF ODD) PROBLEM. %R A3057 PC11 1-3 73. %I A3033 N1035.5 %S A3033 1,3,7,9,63,63,168,322,322,1518,1518,1680 %N A3033 EVERY SEQ OF 4 NUMBERS > A(N) CONTAINS A PRIME > P(N). %R A3033 AMM 79 108772. %I A3231 N1035.8 %S A3231 1,3,7,10,14,18,21,25,28,32,36,39,43,47,50,54,57,61,65,68,72,75,79, %T A3231 83,86,90,94,97,101,104,108,112,115,119,123,126,130,133,137,141,144,148 %N A3231 RELATED TO A BEATTY SEQUENCE. %R A3231 FQ 11 385 73. %I A3512 N1037.5 %S A3512 1,3,7,11,14,18,22,26,29,33,37,41,44,48,52,55,59,63,67,70,74,78,82, %T A3512 85,89,93,97,100,104,108,111,115,119,123,126,130,134,138,141,145,149,153 %N A3512 A BEATTY SEQUENCE. %R A3512 DM 2 338 72. %C N1044 N1044 %N N1044 PRIME NUMBERS OF MEASUREMENT, A SELF-GENERATING SEQUENCE. %R N1044 PCPS 21654 23。AMM 75 80,68。AND1. %Q A1203 N1054 %R A1203 MTAC 25 403 71. %I A3478 N1062.5 %S A3478 1,3,7,17,39,85,183,389,815,1693,3495,7173,14655,29837,60567,122645, %T A3478 247855,500061,1007495,2027493,4076191,8188333,16437623,32978613,66132495 %N A3478 FROM FOLDING A STRIP OF PAPER. %R A3478 DA4. %I A3440 N1064.5 %S A3440 1,3,7,17,42,104,259,648,1627,4098,10350,26202,66471,168939,430071, %T A3440 1096451,2799072,7154189,18305485,46885179,120195301,308393558,791882862 %N A3440 BINARY VECTORS WITH RESTRICTED REPETITIONS. %R A3440 KAP1. %I A3097 N1070.5 %S A3097 1,3,7,20,52,157 %N A3097 CRITICAL CONNECTED TOPOLOGIES. %R A3097 JCT 15B 193 73. %I A3449 N1076.5 %S A3449 1,3,7,24,74,259,891,3176,11326,40942,148646,543515 %N A3449 DISSECTIONS OF A POLYGON. %R A3449 REA1. %I A3083 N1077.5 %S A3083 1,3,7,27,106,681,5972,88963,2349727 %N A3083 RELATED TO NUMBER OF GRAPHS. %R A3083 HA8 91. %I A3260 N1078.5 %S A3260 1,3,7,31,127,89,8191,131071,524287,178481,2089,2147483647, %T A3260 616318177,164511353,2099、863、132645、2039、439、1320、34、1780、337、37、n、A32、MelSeNe数的最大因子。MTAC 21 87,67。BR2 149μ.C.A2585 N1081%S S A2585 1、3、7、3、1212、31、129、727、737、637、332、311、2005、60490、1316764、1、T、A2585、10717017833、9583135931380818118561876186030118262637、261、N、A2585最大因子2.3.5.7+1,r,A2585,SMA 14,26,48。KR2 2。MTAC 26 56872。[%%Q N1085 N1085·%NR85 N1085 MU4 38π%A3038,1,3,8,10,14,15,21,24,28,35,36,45,48,52,55,63,66,78,80,91,99,105,T %A3038,120133,1361331631615816178195210242122452552552562688300,%A3038维的简单李代数。%R A3038 JA3 146。MMAG 48 93×75BAMS 78 637 72. %I A3157 N1088.8 %S A3157 1,3,8,11,14,19,24,29,32,35,40,43,46,51,54,57,62,67,72,75,78,83,88, %T A3157 93,96,99,104,109,114,117,120,125,128,131,136,139,142,147,152,157,160 %N A3157 A SELF-GENERATING SEQUENCE. %R A3157 FQ 10 500 72. %I A3234 N1088.9 %S A3234 1,3,8,11,16,19,21,24,29,32,37,42,45,50,53,55,58,63,66,71,74,76,79, %T A3234 84,87,92,97,100,105,108,110,113,118,121,126,129,131,134,139,142,144,147 %N A3234 RELATED TO FIBONACCI REPRESENTATIONS. %R A3234 FQ 11 385 73. %C N1100 N1100 %S N1100 1,3,8,20,48,112,256,576,1280,2816,6144,13312,28672,61440,131072, %T N1100 278528,589824,1245184,2621440,5505024,11534336,24117248,50331648 %N N1100 (N+3)2**N. %R N1100 PRSE 62 190 46. AS1 795 .I % AI 999 N1100.5%S S A29 99 1、3 8 8、20、5012632、1875 775、154、104、184、136、136、333、1057、18534、66、T % At 99 A2 99 5623 836 3638、1838年1月1日、1月1日、54年、1月5日、1月5日、1月5日、1月5日、1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月1日、1年1月3日、1年1月1日、1年1月1日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年1月3日、1年3天、1年3天、1年3天、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1天1小时、1JSIAM 17 254,69。BAL2 714. %I A3227 N1102.3 %S A3227 1,3,8,22,58,160,434,1204,3341,9363,26308,74376,210823,599832, %T A3227 1710803,4891876,14015505,40231632,115669419,333052242,960219974 %N A3227 ENDPOINTS IN PLANTED TREES. %R A3227 HA9. %I A3101 N1102.5 %S A3101 1,3,8,22,65,209,732,2780,11377,49863,232768,1151914,6018785, %T A3101 33087205,190780212,1150653920,7241710929,47454745803,323154696184 %N A3101 SUM OF K**(N-K+1), K=1,...,N. %R A3101 HWG. %I A3470 N1109.5 %S A3470 1,3,8,31,147,853,5824,45741,405845,4012711,43733976,520795003, %T A3470 6726601063,93651619881,1398047697152,22275111534553,377278848390249 %N A3470 A(N) = NA(N-1) - A(N-2) + 1 + (-1)**N. %R A3470 RI1. %I A3216 N1111.5 %S A3216 1,3,8,48,383,6020 %N A3216 HAMILTONIAN GRAPHS. %R A3216 PL2 4 266 73. %C N1115 N1115 %N N1115 CROSSING NUMBER OF THE COMPLETE GRAPH. %R N1115 GU2. 9,24,6114335247768831,3047 259848 477 91159,% %T A3262 1688 83683573546617179090308966053133189118049 %N A3262在第n个导数项中。% %R A3262 Cr 278 250 250。AMM 80 53 53MTAC 29 216,75。VEH1. %I A3409 N1132.5 %S A3409 1,3,9,30,105,378,1386,5148,19305 %N A3409 CONNECTED LADDER GRAPHS. %R A3409 DM 9 355 74. %Q N1133 N1133 %R N1133 PL2 4 180 73. %Q N1138 N1138 %R N1138 MU4 38. %I A3225 N1139.3 %S A3225 1,3,9,89,1705,67774 %N A3225 SUPERPOSITIONS OF CYCLES. %R A3225 AM1 131 143 73. %I A3166 N1139.5 %S A3166 1,3,9,4523,11991,18197,141683,1092489,20457529,143784081,331130809, %T A3166 20074072489,1193532215121 %N A3166 SQUARE IS A PALINDROME TO BASE 2. %R A3166 JRM 5 13 72. %I A3441 N1141.5 %S A3441 1,3,10,30,99,335,1144,3978,14000,49742,178296,643856,2340135 %N A3441 DISSECTIONS OF A POLYGON. %R A3441 REA1. %Q N1152 N1152 %R N1152 PL2 4 180 73. %I A3060 N1157.5 %S A3060 1,3,11,27,101,41,7,239,73,81,451,21649,707,53,2629,31,17,2071723,19 %N A3060 SMALLEST NUMBER WITH RECIPROCAL OF PERIOD N. %R A3060 PC1 1 4-13 73. %C N1164 N1164 %S N1164 1,3,11,49,261,1631,11743,95901,876809,8877691,98641011,1193556233, %T N1164 15624736141,220048367319,3317652307271533、1941、8114、1499、846328、1473、7%A(n+1)=n(a(n)+a(n-1)+…)+1,r r n1164 cjm 22 26 70。Ad1 70 A.151N17170.5%S S A31 15 1,3 111131757 176627 51 12788 4328 72039 7739 113849 605,% T A31 15 75 68 49 978 79 875 34 390 904 904 33 174 949 179 880 10255981A %(n+2)=(4×*(n+1)-5)a(n)-4a(n-2).% %R a31 15 dHL。H.P.N1174N1174,N1174,N1174,N1174,1,3,12,55,2,2,2,3,4,198,1,883057,2,2 82306,1,2,2,2,4,5,4,5,4,5,4,2,2,30,5,3,5,3,3,3,3,4,4,5,4,N,N1174二项式系数C(3N,N-1)/N。EMN 32 5,40。CMA2 25 70。男人191 98,71。FQ 11 125,73。DM 9 355 74. %I A3316 N1177.5 %S A3316 1,3,12,58,335,2261,17465,152020,1473057,15730705,183571817, %T A3316 2324298010,31737207026,464904410985,7272666016725,121007866402968 %N A3316 SUM OF LENGTHS OF LONGEST INCREASING SUBSEQUENCES OF ALL PERMUTATIONS OF N THINGS. %R A3316 MTAC 22 390 68. %I A3483 N1177.7 %S A3483 1,3,12,60,270,1890,14280,128520,1096200,12058200,139043520, %T A3483 1807565760 %N A3483 SQUARE PERMUTATIONS. %R A3483 JCT 17A 156 74. %C N1179 N1179 %N N1179 FACTORIAL(N)/2. %R N1179 PEF 77 26 62. %C N1183 N1183 %N N1183 10 IS A QUADRATIC RESIDUE MODULO P AND CLASS OF MANTISSA IS 2. %R N1183 KR11 61. %I A3319 N1188.5 %S A3319 1,3,13,71,461,3447,29093,273343,2829325,31998903,392743957, %T A3319 5201061455,73943424413,1123596277863,18176728317413,311951144828863 %N A3319 A(N) = FACTORIAL(N) - SUM OF A(N-K).FACTORIAL(K). %R A3319 CR 275 569 72. %I A3169 N1202.5 %S A3169 1,3,14,79,494,3294,22952,165127,1217270,9146746,69799476,539464358, %T A3169 4214095612,33218794236,263908187100,2110912146295,16985386737830 %N A3169 2-LINE ARRAYS. %R A3169 FQ 11 124 73. %I A2966 N1203.5 %S A2966 1,3,14,147,3462 %N A2966 REPRESENTATIONS OF 1 AS A SUM OF UNIT FRACTIONS. %R A2966 SI3. %C N1208 N1208 %S N1208 1,3,15,60,260,1092,4641,19635,83215,352440,1493064,6324552, %T N1208 26791505,113490195,480752895,2036500788,8626757644,36543528780 %N N1208 FIBONOMIAL COEFFICIENTS. %R N1208 FQ 6 82 68. BR1 74. %I A3448 N1212.5 %S A3448 1,3,15,81,422,2124,10223,47813,218130,977354,4315130,18833538 %N A3448 DISSECTIONS OF A POLYGON. %R A3448 REA1. %C N1215 N1215 %S N1215 1,3,15,104,164,194,255,495,584,975,2204,2625,2834,3255,3705,5186, %T N1215 5187,10604,11715,13365,18315,22935,25545,32864,38804,39524,46215,48704 %N N1215 PHI(N) = PHI(N+1). %R N1215 AMM 56 22 49. MI2. %I A3276 N1215.5 %S A3276 1,3,15,104,495,975,22935,32864,57584,131144,491535 %N A3276 RESIDUES MOD N ARE ISOMORPHIC TO RESIDUES MOD N+1. %R A3276 MTAC 27 448 73. %I A3505 N1218.5 %S A3505 1,3,15,203,3785 %N A3505 SIMPLE TOURNAMENTS. %R A3505 DM 11 65 75. %C N1230 N1230 %S N1230 1,3,16,547,538811,620245817465,692770666469127829226736, %T N1230 1025344764595988314871439243086711931108916434521 %N N1230 CONVERGENTS TO LEHMER'S CONSTANT. %R N1230 DMJ 4 334 38. JWW.I.A3122 N1232.5%S A3122,1,18136117010961298813131298923013306060155839 2462 62 %%A3122哈密顿根三角剖分。% %R A3122 DM 6 167 73。JCT 14A 6 73. %Q N1244 N1244 %R N1244 PL2 4 180 73. %I A3111 N1244.5 %S A3111 1,3,19,225,3441,79259,2424195 %N A3111 SPECIAL PERMUTATIONS. %R A3111 JNT 5 48 73. %Q N1245 N1245 %R N1245 PL2 4 180 73. %I A3011 N1245.5 %S A3011 1,3,19,271,7365,326011,21295783,1924223799 %N A3011 PERMUTATIONS OF OBJECTS ALIKE IN PAIRS. %R A3011 R1 17. %I A3150 N1248.5 %S A3150 1,3,20,364,17017,2097018,674740506,568965009030,1255571292290712, %T A3150 7254987185250544104,109744478168199574282739 %N A3150 FIBONOMIAL CATALAN NUMBERS. %R A3150 FQ 10 363 72. %I A3443 N1257.5 %S A3443 1,3,24,150,825,4205,20384,95472,436050,1954150,8629528,37665030 %N A3443 DISSECTIONS OF A POLYGON. %R A3443 REA1. %I A3236 N1258.5 %S A3236 1,3,24,320,6122,153762,4794664,178788528,7762727196,384733667780, %T A3236 21434922419504,1326212860090560,90227121642144424,6694736236093168200 %N A3236 SUM OF (-1)**(N-K).C(N,K).C((K+1)**2,N). %R A3236 HWG. %I A3024 N1261.5 %S A3024 1,3,25,543,29281,3781503,1138779265,783702329343,1213442454842881, %T A3024 4175098976430598143 %N A3024 ACYCLIC DIGRAPHS. %R A3024 HA7 254. %I A3466 N1263.5 %S A3466 1,3,28,210,1506,10871,80592,618939,4942070,41076508,355372524, %T A3466 3198027157,29905143464,290243182755,2920041395248,30414515081650 %N A3466 MINIMAL COVERS. %R A3466 DM 5 249 73. %I A3190 N1265.5 %S A3190 1,3,29,2101,7011349,1788775603133,53304526022885278659 %N A3190 CONNECTED 2-PLEXES. %R A3190 DM 6 384 73. %I A3129 N1269.5 %S A3129 1,3,33,270,2025,14868,109851,827508,6397665 %N A3129 TRANSFER IMPEDANCES OF AN N-TERMINAL NETWORK. %R A3129 BSTJ 18 301 39. %I A3029 N1278.3 %S A3029 1,3,48,3400,955860,1034141596,4338541672792,71839019692720536 %N A3029 UNILATERALLY CONNECTED DIGRAPHS. %R A3029 HA7 270. %I A3028 N1278.6 %S A3028 1,3,51,3614,991930,1051469032,4364841320040,71943752944978224 %N A3028 DIGRAPHS WITH A SOURCE. %R A3028 HA7 270. %I A3027 N1279.5 %S A3027 1,3,54,3834,1027080,1067245748,4390480560744,72022346390883864 %N A3027 WEAKLY CONNECTED DIGRAPHS. %R A3027 HA7 270. %I A3009 N1286.5 %S A3009 1,3,147,1383123,489735485064147,245597025618959718190041238775763, %T A3009 247062114274836300381127305147102564467751924522387062291401805739987 %N A3009 A(N) = A(N-1) + (A(N-1).2**(N-2))**2. %R A3009 JLMS 28 286 53. %I A3194 N1289.5 %S A3194 1,4,0,0,0,8,0,112,256,156,896,3536,5472,5400,49088,115008,47776, %T A3194 555492,1976736,2563424,4446272,29452776,61952896,4795392,374024448 %N A3194 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3194 JMP 6 298 65. 物理学家6,1511,73,.12%N1290,N1290,%S,N1290,1,4,0,0,8,601444,1248,4132,248429,3680724524401480944,%,T N1290,48 836,161,147845,76696177637,24%8%N N1290对立方晶格的敏感性。%的R N1290 JMP 6 298 65。A29 78、1、4、0、12、8、12、8、12、8、8、48、3、48、3、8、8、68、68、88、6、6、48、768、48、n、N、A29对蜂窝状体的敏感性。物理6,1511,73PHYSA 6 1511 73. %I A2979 N1290.6 %S A2979 1,4,0,16,32,156,608,2688,12064,55956,266656 %N A2979 SUSCEPTIBILITY FOR SQUARE LATTICE. %R A2979 PHYSA 5 636 72. %I A3415 N1291.5 %S A3415 1,4,1,5,1,12,6,7,1,16,1,9,8,32,1,21,1,24,10,13,1,44,10,15,27,32,1, %T A3415 31,1,80,14,19,12,60,1,21,16,68,1,41,1,48,39,25,1,112,14,45,20,56,1,81 %N A3415 A(1)=0, A(PRIME)=1, A(MN)=MA(N)+NA(M). %R A3415 CMB 4 117 61. CCMN 5(8)6 73 .I A29 49、1、4、2、7、350、1、5、5、1、1、1、1、1、1、1、1、1、1、1、1、3、3、30、4、10、15、8、1、2、1、1、2、1、1、1、1、1、1、1、1、1、1、1、1、1、1、1、1、1、1、1、2、1、2、1、2、1、2、18、1、2、2、10、14、3、1、%1、29、3、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、1、2、2、1、2、3、1、3、1、3、1、2、3、1、2、3、1、2、3、1、2、3、1、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、2、1、2、2、2、2、2、2、2、2、1、2、1、2、2、2、2、2、2、2、2、2、2、2、1、2、1、2、1、2、2、2、2、2、2、2、2、2、2、2、2、2、2、73、1、3、1、2、2、2、73、73、2、3、2、2、2、2、2JSH. %I A3156 N1307.5 %S A3156 1,4,5,6,9,12,15,16,17,20,21,22,25,26,27,30,33,36,37,38,41,44,47,48, %T A3156 49,52,55,58,59,60,63,64,65,68,69,70,73,76,79,80,81,84,85,86,89,90,91,94 %N A3156 A SELF-GENERATING SEQUENCE. %R A3156 FQ 10 500 72. %I A2970 N1310.5 %S A2970 1,4,5,10,16,19,20,26,29,31,35,41,43,49,50,55,56,59,70,71,80,85,94, %T A2970 95,100,101,106,109,110,121,149,154,160,166,175,179,184,190,191,200,205 %N A2970 (2N)**2 + 9 IS PRIME. %R A2970 KK1 1. %C N1313 N1313 %N N1313 THE NO-THREE-IN-LINE PROBLEM. %R N1313 GU3. WE1 124。CM2 7. %I A3259 N1323.5 %S A3259 1,4,6,9,11,14,17,19,22,25,27,30,32,35,38,40,43,45,48,51,53,56,59, %T A3259 61,64,66,69,72,74,77,79,82,85,87,90,93,95,98,100,103,106,108,111,114,116 %N A3259 RELATED TO FIBONACCI REPRESENTATIONS. %R A3259 FQ 11 386 73. %I A3264 N1323.8 %S A3264 1,4,6,9,12,14,17,19,22,25,27,30,33,35,38,40,43,46,48,51,53,56,59, %T A3264 61,64,67,69,72,74,77,80,82,85,88,90,93,95,98,101,103,106,108,111,114 %N A3264 NOT REPRESENTABLE BY TRUNCATED FIBONACCI SEQUENCE. %R A3264 BR1 62. %C N1325 N1325 %N N1325 FLEXAGONS. %R N1325 AMM 64 153 57. n=φ(n+1)=%A361 N1331.2%S.A34 61、1、4、7、10、16、28、521001968、740766、148121229、2245、8049 156、πA34 61 983061966、12739、20783636、15728、56、56、2、3.2、4、3.2、3.2。Rea1.C%A1494138%%N-A1494PHIMCL1. %I A2974 N1331.5 %S A2974 1,4,7,11,20,35,59,99,165,270,443 %N A2974 RESTRICTED SOLID PARTITIONS. %R A2974 JCT 13A 144 72. %I A3404 N1332.5 %S A3404 1,4,7,14,23,41,63,104,152,230,327,470,647,897,1202,1616,2117,2775, %T A3404 3566,4580,5787,7301,9092,11298,13885,17028,20688,25076,30154,36172,43094 %N A3404 CERTAIN PARTIALLY ORDERED SETS OF INTEGERS. %R A3404 LMS13 123. %I A3451 N1340.2 %S A3451 1,4,8,16,25,40,56,80,105,140,176,224 %N A3451 DISSECTIONS OF A POLYGON. %R A3451 REA1. %I A3199 N1340.5 %S A3199 1,4,8,16,32,54,100,182,328,494,984,1572,2656,4212,8162 %N A3199 CLUSTER SERIES FOR HONEYCOMB. %R A3199 PRV 133 A315 64. DG2 225 .0%D N1341 N1341%I IA3049 N1345.5%S S A3049,1,4,8,37 184,%N A3049连接的Euler图。%%R A3049 PTGT 151。VE1 6 46 46。MR 44 1195(6557) 72.HA8 117. %I A2993 N1347.5 %S A2993 1,4,9,1,2,3,4,6,8,1,1,1,1,1,2,2,2,3,3,4,4,4,5,5,6,6,7,7,8,9,9,1,1, %T A2993 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4 %N A2993 INITIAL DIGITS OF SQUARES. %R A2993 %I A3132 N1349.5 %S A3132 1,4,9,16,25,36,49,64,81,1,2,5,10,17,26,37,50,65,82,4,5,8,13,20,29, %T A3132 40,53,68,85,9,10,13,18,25,34,45,58,73,90,16,17,20,25,32,41,52,65,80,97 %N A3132 SUM OF SQUARES OF DIGITS OF N. %R A3132 CJM 12 374 60. %I A3086 N1376.5 %S A3086 1,4,10,136,720,44224,703760 %N A3086 SELF-COMPLEMENTARY DIGRAPHS. %R A3086 HA8 140. %I A3250 N1377.2 %S A3250 1,4,11,15,22,26,29,33,40,44,51,58,62,69,73,76,80,87,91,98,102,105, %T A3250 109,116,120,127,134,138,145,149,152,156,163,167,174,178,181,185,192,196 %N A3250 RELATED TO FIBONACCI REPRESENTATIONS. %R A3250 FQ 11 385 73. %I A3146 N1377.5 %S A3146 1,4,11,17,24,28,35,41,48,55,61,68,72,79,85,92,98,105,109,116,122, %T A3146 129,136,142,149,153,160,166,173,177,184,190,197,204,210,217,221,228,234 %N A3146 A SELF-GENERATING SEQUENCE. %R A3146 FQ 10 49 72. %I A3230 N1382.5 %S A3230 1,4,11,28,67,152,335,724,1539,3232,6727,13900,28555,58392,118959, %T A3230 241604,489459,989520,1997015,4024508,8100699,16289032,32726655,65705268 %N A3230 FROM FOLDING A STRIP OF PAPER. %R A3230 DA4. %C A2387 N1385 %S A2387 1,4,11,31,83,227,616,1674,4550,12367,33617,91380,248397,675214, %T A2387 1835421,4989191,13562027,36865412,100210581,272400600,740461601 %N A2387 A(N) TERMS OF HARMONIC SERIES EXCEED N. %R A2387 AMM 78 870 71. HP.I %A33N1392.5%S A333,1,4,12,24,5210822441284151533152%N 3A3 3系列方晶格,%%R A33PRV 133 A315 64。DG2 225 n.98 N1398 N1398,S N1398,1,4,12,32,8019242404241,2012462457,56338811468,,% T N1398 2457 60524248111412524968073680757 6060220200,9661313734 4%%N N1398(N+ 1)2×N N %,R N1398 PRSE 62 190 46。BMTA 46 422,59。AS1 796. %C N1401 N1401 %S N1401 1,4,12,36,100,276,740,1972,5172,13492,34876,89764,229628,585508, %T N1401 1486308,3763460,9497380,23918708,60080156,150660388,377009300,942105604 %N N1401 SUSCEPTIBILITY FOR SQUARE LATTICE. %R N1401 PHYSA 5 629 72. %C N1402 N1402 %N N1402 WALKS ON A SQUARE LATTICE. %R N1402 PHYSA 5 659 72. %I A3212 N1402.3 %S A3212 1,4,12,36,108,264,708,1668,4536,10926,28416 %N A3212 CLUSTER SERIES FOR DIAMOND LATTICE. %R A3212 PRV 133 A315 64. DG2 225. %I A3119 N1402.5 %S A3119 1,4,12,36,108,324,948,2772,8076,23508,67980,196548,566820,1633956, %T A3119 4697412,13501492,38742652,111146820,318390684,911904996,2608952940 %N A3119 SUSCEPTIBILITY FOR DIAMOND LATTICE. %R A3119 PHYSA 6 1520 73. %I A2996 N1403.5 %S A2996 1,4,12,41,126,428,1416,4857,16753,58785,207868,742899,2674010, %T A2996 9694799,35356240,129644789,477633711,1767263189,6564103612,24466266587 %N A2996 IRREDUCIBLE ARRANGEMENTS OF PARENTHESES. %R A2996 MAB (2) VOL 11, NUMBER 6,PAGE 13. CRB 109. %I A3444 N1403.8 %S A3444 1,4,12,43,143,504,1768,6310,22610,81752,297160,1086601 %N A3444 DISSECTIONS OF A POLYGON. %R A3444 REA1. %I A3462 N1408.5 %S A3462 1,4,13,40,121,364,1093,3280,9841,29524,88573,265720,797161,2391484, %T A3462 7174453,21523360,64570081,193710244,581130733,1743392200,5230176601 %N A3462 (3**N - 1)/2. %R A3462 %I A3117 N1411.5 %S A3117 1,4,14,2,1,1,3,2,29,2,1,7,1,5,2,1,1,19,12,77,2,16,2,1,1,15,1,1,3, %T A3117 14,5,1,3,2,1,1,1,1,1,1,5,1,463,1,379,3,5,3,11,1,7,7,1,1,2,1,1,1,2,1,1,1 %N A3117 CONTINUED FRACTION EXPANSION OF FIFTH ROOT OF 3. %R A3117 HPR. JS.N.15N1415,N1415,N1415,N1415,1416722072207254194440626811886404345 965,% T N1415 15967 9809594230189118811985 57 9095404011338026180425500 29 600 600 %,N N1415 C(2N+ 1,N-1)。4 /(N+ 3)。1841,414141435171758%N3A3184非退化阈值函数.%A3010N147.5%S S A3010,1,4,1419437,1616317954,55654,68,227 46114,% %T A3010 4023 8616740360602225635565610210099 4%%N A3010A(n)=A(N-1)** 2 - 2。%,R A3010 DI2 1 397。WA1.1.0%I A3184N14173%Sa3JLMS 28 285 53。FQ 11 N1421 N1421、NS21、N1421、S、N1421、1、4、15、562、107923、14404375、1679660664、6624961449、65 77.00、% T N1421 314421602654、5657、527、227、202、3039、432、517、517、517、3、7、7、8、8、6、10、0、N、N、N1421二项系数C(2N、N-1)。AS1 828。PL2 1 292 70. %I A3126 N1421.5 %S A3126 1,4,15,58,226,882,3457,13606,53683 %N A3126 VALUE OF AN URN. %R A3126 DM 5 307 73. %I A3471 N1431.5 %S A3471 1,4,16,80,672,4752,48768,440192,5377280,59245120,839996160, %T A3471 10930514688,176547098112,2649865335040,48047352500224,817154768973824 %N A3471 PERMUTATIONS WITH NO HITS ON 2 MAIN DIAGONALS. %R A3471 R1 187. %I A3127 N1433.5 %S A3127 1,4,17,70,282,1136,4583,18457,74131 %N A3127 VALUE OF AN URN. %R A3127 DM 5 307 73. %I A3474 N1434.5 %S A3474 1,4,18,32,160,324,1456,2048,13122,25600,117128,209952,913952, %T A3474 2119936,9447840,13107200,86093440 %N A3474 GENERALIZED PHI FUNCTION. %R A3474 MTAC 28 1168 74. %I A3134 N1443.5 %S A3134 1,4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,1,2,1,2,1,39,2,1,1,1,13, %T A3134 1,2,1,30,1,1,1,3,2,5,4,1,5,1,5,1,2,1,1,94,6,2,19,11,1,60,1,1,50,2,1,1,8 %N A3134 CONTINUED FRACTION EXPANSION OF 2COS(2PI/7). %R A3134 JRAM 255 128 72. %I A3489 N1444.5 %S A3489 1,4,20,84,292,980,3052,9316,27396,79412 %N A3489 SUSCEPTIBILITY FOR SQUARE LATTICE. %R A3489 DG2 136. %C N1445 N1445 %N N1445 FACTORIAL(N)/6. %R N1445 PEF 77 44 62. %I A3168 N1449.5 %S A3168 1,4,21,126,818,5594,39693,289510,2157150,16348960,125642146, %T A3168 976789620,7668465964,60708178054,484093913917,3884724864390 %N A3168 SUM OF C(N,K)C(2N+K,K-1)/N, K=1,...,N. %R A3168 FQ 11 123 73. %I A3287 N1454.5 %S A3287 1,4,22,140,970,7196,56092,452064,3735700,31484244,269613896 %N A3287 WALKS ON A CUBIC LATTICE. %R A3287 PHYSA 6 351 73. %I A3288 N1458.5 %S A3288 1,4,24,152,1080,8152,63976,518232,4299728,36360872,312284536 %N A3288 WALKS ON A CUBIC LATTICE. %R A3288 PHYSA 6 351 73. %C N1476 N1476 %S N1476 1,4,29,355,6942,209527,9535241,642779354 %N N1476 LABELED TOPOLOGIES OR TRANSITIVE DIGRAPHS. %R N1476 CACM 10 296 67. Purb 19240 68。JA1 8 194 194。HA8 243 .A.C.A1761 N1478α%N A1761球的解剖。% %R A1761 CMA 2 25 25。MAN 191 98 71. %I A3436 N1479.5 %S A3436 1,4,31,293,3326,44189,673471,11588884,222304897,4704612119, %T A3436 108897613826,2737023412199,74236203425281,2161288643251828 %N A3436 HAMILTONIAN CIRCUITS ON N-OCTAHEDRON. %R A3436 SI4. %I A3488 N1488.5 %S A3488 1,4,36,232,1308,6808,33560,159108 %N A3488 SUSCEPTIBILITY FOR TRIANGULAR LATTICE. %R A3488 DG2 136. %Q N1503 N1503 %R N1503 MU4 38. %C N1508 N1508 %S N1508 1,4,56,9408,16942080,535281401856,377597570964258816 %N N1508 REDUCED LATIN SQUARES. %R N1508 R1 210. RYS 53。FY1 22。RMM 193。JCT 3 98 67.DM 11 94 75. %C A0316 N1513 %S A0316 1,4,80,4752,440192,59245120,10930514688,2649865335040, %T A0316 817154768973824,312426715251262464,145060238642780180480 %N A0316 PERMUTATIONS WITH NO HITS ON 2 MAIN DIAGONALS. %R A0316 R1 187. %I A3135 N1526.5 %S A3135 1,5,1,42,1,3,24,2,2,1,16,1,11,1,1,2,31,1,12,5,1,7,11,1,4,1,4,2,2,3, %T A3135 4,2,1,1,11,1,41,12,1,8,1,1,1,1,1,9,2,1,5,4,1,25,4,6,11,1,4,1,6,1,1,1,2 %N A3135 CONTINUED FRACTION EXPANSION OF ROOT OF X**5 - X - 1. %R A3135 JRAM 255 13072. %I A3273 N1530.3 %S A3273 1,5,6,7,13,14,15,20,21,22,23,24,28,29,30,31,34,37,38,39,41,45,46, %T A3273 47,52,53,54,55,56,60,61,62,63,65,69,70,71,77,78,79,80,84,85,86,87,88,92 %N A3273 CONGRUENT NUMBERS. %R A3273 MTAC 28 304 74. %I A3226 N1530.5 %S A3226 1,5,6,25,76,376,625,9376,90625,109376,890625,2890625,7109376, %T A3226 12890625,87109376,212890625,787109376,1787109376,8212890625,18212890625 %N A3226 AUTOMORPHIC NUMBERS: N SQUARED ENDS IN N. %R A3226 JRM 1 178 68. %I A3429 N1536.5 %S A3429 1,5,7,15,27,57,114,243,506,1102,2381,5269,11686,26277,59348,135317, %T A3429 310064,715475,1659321,3870414,9071915,21372782,50591199,120332237 %N A3429 TREES BY STABILITY INDEX. %R A3429 CM2 51. %C A2596 N1538 %S A2596 1,5,7,21,33,429,715,2431,4199,29393,52003,185725,334305,9694845, %T A2596 17678835,64822395,119409675,883631595,1641030105,6116566755,11435320455 %N A2596 FROM DOUBLE FACTORIALS. %R A2596 RG1 415. %I A3246 N1539.5 %S A3246 1,5,8,12,13,17,21,24,28,29,33,37,41,44,57,73,76. %N A3246 REAL QUADRATIC EUCLIDEAN FIELDS (A FINITE SEQUENCE). %R A3246 LE3 2 57. AMM 75948 68。ST5 294. %I A3147 N1558.5 %S A3147 1,5,11,19,31,41,59,61,71,79,109,131,149,179,191 %N A3147 PRIMES WITH A FIBONACCI PRIMITIVE ROOT. %R A3147 FQ 10 164 72. %C N1569 N1569 %S N1569 1,5,13,27,48,78,118,170,235,315,411,525,658,812,988,1188,1413,1665, %T N1569 1945,2255,2596,2970,3378,3822,4303,4823,5383,5985,6630,7320,8056,8840 %N N1569 [N(N+2)(2N+1)/8]. %R N1569 MAG 46 55 62. MAG 55 440,71。MMAG 47 290 74. %I A3248 N1572.5 %S A3248 1,5,14,20,29,35,39,45,54,60,69,78,84,93,99,103,109,118,124,133,139, %T A3248 143,149,158,164,173,182,188,197,203,207,213,222,228,237,243,247,253,262 %N A3248 RELATED TO FIBONACCI REPRESENTATIONS. %R A3248 FQ 11 385 73. %I A3295 N1586.5 %S A3295 1,5,17,46,116,252,533,1034,1961 %N A3295 COEFFICIENTS OF A MODULAR FUNCTION. %R A3295 GMJ 8 29 67. %C A2826 N1593 %N A2826 PRECOMPLETE POST FUNCTIONS. %R A2826 SMD 10 619 69. JCT-14A 6 73 .I.A396N1594.5%S S A329 6,1,5,19,631853070469968 15335%,A329,模函数的系数为:%%R A329 6GMJ 8 29 67。MTAC 29 216,75。We 1.07C N1607 N1607,N1607,1,5,21,8433012505194575,8529,30301,1440664,445,%,T N1607 1738 38 606 39 15265 182525 1037 1583540592595015905367810%,N N1607二项系数C(2N+ 1,N-1),% %R N1607 Cay1 13 95。AS1 828。Rea1.nC08 N1608 N1608 NS08、1、5、21、85、34、6、1、6、45、6、45、45、48、1349、1349、2513、99、815、155、924、0 % T N1608、223 696218947、875、3579139、43161676567、266、2306、122、9064、924、2245、4、1、3。FMR 1 112。RCI 217 .0%C A2582165,23,1771950917531795123513779001515359333,% %T A258817829,1525968,802523,1,14,25。MTAC 26 570 72. %I A3487 N1614.5 %S A3487 1,5,23,527,277727,77132286527,5949389624883225721727, %T A3487 35395236908668169265765137996816180039862527 %N A3487 A(N) = A(N-1)**2 - 2. %R A3487 JSH1. %I A3224 N1618.5 %S A3224 1,5,24,391,9549,401691 %N A3224 SUPERPOSITIONS OF CYCLES. %R A3224 AM1 131 143 73. %C A2050 N1622 %S A2050 1,5,25,149,1081,9365,94585,1091669,14174521,204495125,3245265145, %T A2050 56183135189,1053716696761,21282685940885,460566381955705 %N A2050 A SUM INVOLVING STIRLING NUMBERS. %R A2050 SKA 11 95 28. MMAG 37 132 64. %D A2023 N1623 %I A3467 N1627.5 %S A3467 1,5,28,190,1340,9065,57512,344316,1966440,10813935,57672340, %T A3467 299893594,1526727748,7633634645,37580965520,182536112120,876173330832 %N A3467 MINIMAL COVERS. %R A3467 DM 5 249 73. %C A2584 N1628 %S A2584 1,5,29,19,2309,30029,8369,929,46027,81894851,876817,38669, %T A2584 304250263527209,92608862041,59799107,1143707681,69664915493 %N A2584 LARGEST FACTOR OF 2.3.5.7... - 1 .%的R A2588SMA 14 26 26。KR2 2。MTAC 26 568,72。MMAG 48 93,75。26545 249490174040957 826,πT A3515 9601949499594984226533265330249475 947 727 5888 748 83%%A3515系列减少连通图。JL.I.%A3515N1637.5%S S A3515,1,5,513634 31711973161880PA2. %I A3482 N1652.7 %S A3482 1,5,39,272,1869,12815,87840,602069,4126647,28284464,193864605, %T A3482 1328767775,9107509824,62423800997,427859097159,2932589879120 %N A3482 A(N) = 7A(N-1) - A(N-2) + 4. %R A3482 DM 9 89 74. %C N1653 N1653 %S N1653 1,5,40,260,1820,12376,85085,582505,3994320,27372840,187628376, %T N1653 1285992240,8814405145,60414613805,41408893560,2838203264876 %N N1653 FIBONOMIAL COEFFICIENTS. %R N1653 FQ 6 82 68. 14621919105165969169991691693249%%A3084D与有向图的数目有关。% %R R A3084HA8 124πA3565 N16695%S S A3565,510932 9721279223 737 2023 9703629 89%,% T A34 65 17014118604696121636123612929 966 66 89125%N A34 65覆盖一套。% %R A34 65 PL2 4 515 73。BR1 74μ.I A30841654.5%S A3081,5404080DM 5、247、第五、1、2、1、2、1、1、1、1、1、1、3、3、3、3、3、7、2、15、2、2、4、16、2、7、1、1、1、10、1、1、1、1、10、1、1、1、1、1、1、14、1、2、4、2、1、1、1、17、1、3、3、4、1、3、1、3、2、1、2、33、1、6、1、2、4、1、N、A、N、A29、第五、2、R、A2550、HPR的第五根连续体展开。JS.I.%I,A3155 N17065%,S A3155,1,6,152551897 92263,19726532 13207210,%A3155减半棋盘。% %R A3155 Ga2 189。i %A33 23 N17085%,S A33 23,1,6,17,66 327 % %N A33 23拉姆齐数。% R R A33 23 BE7 175。HWG.I %A32N17103%S.A321,1,618.18126350716864040888 68 %N A32三角晶格簇系列,%R A32PRV 133 A315 64。dg2 225 .i a3198 n170.6μs s a3198,1,6,18,48 126,668,668,16862168621988 843058,%N,A3198簇列为正方晶格,%R R A3198 PRV 133 A315 64。7%%S A32 90、1、6、18、50、156、6、18、242、142、14858934、6、352、6、352、73。DG2 225μ%I A32 90N1710DG2 225. %I A3496 N1712.5 %S A3496 1,6,18,132,810,5724,42156,323352,2550042,20559660,168680196 %N A3496 INTERNAL ENERGY SERIES FOR CUBIC LATTICE. %R A3496 DG2 425. %I A3469 N1725.5 %S A3469 1,6,22,65,171,420,988,2259,5065,11198,24498,53157,114583,245640, %T A3469 524152,1113959,2359125,4980546,10485550,22019865,46137091,96468716 %N A3469 MINIMAL COVERS. %R A3469 DM 5 249 73. %C N1729 N1729 %N N1729 C(N,2).2**(N-2). %R N1729 PRSE 62 190 46. AS1 796。MFM 74 62 70. %C N1730 N1730 %S N1730 1,6,24,90,318,1098,3696,12270,40224,130650,421176,1348998,4299018, %T N1730 13635630,43092888,135698970,426144654 %N N1730 SUSCEPTIBILITY FOR TRIANGULAR LATTICE. %R N1730 PHYSA 5 632 72. %I A3517 N1739.5 %S A3517 1,6,27,110,429,1638,6188,23256,87210,326876,1225785,4601610, %T A3517 17298645,65132550,245642760,927983760,3511574910,13309856820,50528160150 %N A3517 C(2N+1,N-2).6/(N+4). %R A3517 VEH1. %C N1741 N1741 %S N1741 1,6,28,120,495,2002,8008,31824,125970,497420,1961256,7726160, %T N1741 30421755,119759850,471435600,1855967520,7307872110,28781143380 %N N1741 BINOMIAL COEFFICIENTS C(2N,N-2). %R N1741 LA4 517. 14126140141948196208220,21%63042582254226436833533638073808688884420%%A3062开始的周期酉等分序列。AS1 828μ.I A3062 N17465%,S A3062,1,6,30,42,54,60,66,7890901021DG2 225. %C N1750 N1750 %S N1750 1,6,30,138,606,2586,10818,44574,181542,732678,2935218,11687202, %T N1750 46296210,182588850,717395262,2809372302,10969820358 %N N1750 SUSCEPTIBILITY FOR TRIANGULAR LATTICE. %R N1750 PHYSA 5 627 72. %I A3279 N1752.5 %S A3279 1,6,30,144,666,3024,13476,59328,258354,1115856,4784508,20393856, %T A3279 86473548,365034816,1534827960,6431000832,26862228450 %N A3279 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3279 RS3 273 607 73. DG2 404. %C N1753 N1753 %S N1753 1,6,30,150,726,3510,16710,79494,375174,1769686,8306862,38975286, %T N1753 182265822,852063558,3973784886,18527532310,86228667894,401225391222 %N N1753 SUSCEPTIBILITY FOR CUBIC LATTICE. %R N1753 PHYSA 5 651 72. %C N1754 N1754 %S N1754 1,6,30,150,726,3534,16926,81390,387966,1853886,8809878,41934150, %T N1754 198842742,943974510,4468911678,21175146054,100121875974,473730252102 %N N1754 WALKS ON A CUBIC LATTICE. %R N1754 JCP 39 411 63. PHYSA 5 659 72. %I A3463 N1756.2 %S A3463 1,6,31,156,781,3906,19531,97656,488281,2441406,12207031,61035156, %T A3463 305175781,1525878906,7629394531,38146972656,190734863281,953674316406 %N A3463 (5**N - 1)/4. %R A3463 %I A3128 N1756.5 %S A3128 1,6,31,160,856,4802,28337,175896,1146931 %N A3128 DRIVING-POINT IMPEDANCES OF AN N-TERMINAL NETWORK. %R A3128 BSTJ 18 301 39. %I A3423 N1758.5 %S A3423 1,6,34,1154,1331714,1773462177794,3145168096065837266706434, %T A3423 9892082352510403757550172975146702122837936996354 %N A3423 A(N) = A(N-1)**2 - 2. %R A3423 AJM 1 313 1878. DI2 1 376。JSH1. %C A2595 N1768 %S A2595 1,6,40,112,1152,2816,13312,10240,557056,1245184,5505024,12058624, %T A2595 104857600,226492416,973078528,2080374784,23622320128,30064771072 %N A2595 FROM DOUBLE FACTORIALS. %R A2595 RG1 414. %Q A0407 N1784 %R A0407 MAN 191 98 71. %I A3267 N1785.5 %S A3267 1,6,60,1820,136136,27261234,14169550626,19344810307020, %T A3267 69056421075989160,645693859487298425256,15803204856220738696714416 %N A3267 CENTRAL FIBONOMIAL COEFFICIENTS. %R A3267 FQ 6 82 68. BR1 74 .%的C A1763 N1788·%N A1763球的解剖。% %R A1763 CMA 2 25 25。MAN 191 98 71. %I A3235 N1788.5 %S A3235 1,6,72,1322,32550,1003632,37162384,1605962556,79330914540, %T A3235 4409098539560,272297452742304,18499002436677336,1371050716542451672 %N A3235 SUM OF (-1)**(N-K).C(N,K).C(K**2,N). %R A3235 HWG. %C N1791 N1791 %S N1791 1,6,90,1860,44730,1172556,32496156,936369720,27770358330, %T N1791 842090474940,25989269017140,813689707488840,25780447171287900 %N N1791 WALKS ON A CUBIC LATTICE. %R N1791 AIP 9 345 60. RS3 273 586 73. %I A3425 N1794.5 %S A3425 1,6,114,5256,507720,93616560,30894489360 %N A3425 N %R A3425 CM2 21. %I A3460 N1797.5 %S A3460 1,6,154,66344,15471166144,663447306235471066144, %T A3460 1547116614473162154311663447306215471066144 %N A3460 OCTAL FORMULAS FOR DRAGON CURVES. %R A3460 SAM 216(4) 118 67. %I A3191 N1809.5 %S A3191 1,6,5972,1225533120 %N A3191 SYMMETRIC LATIN SQUARES WITH CONSTANT DIAGONAL. %R A3191 JRM 5 202 72. %I A3299 N1813.5 %S A3299 1,7,5,3635,557485,7596391,19681954039,32139541115 %N A3299 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3299 RS3 273 593 73. %I A3282 N1827.2 %S A3282 1,7,19,25,67,205,3389,24469 %N A3282 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3282 RS3 273 590 73. %I A3215 N1827.5 %S A3215 1,7,19,37,61,91,127,169,217,271,331,397,469,547,631,721,817,919, %T A3215 1027,1141,1261,1387,1519,1657,1801,1951,2107,2269,2437,2611,2791,2977 %N A3215 CENTERED HEXAGONAL NUMBERS 3N(N+1)+1. %R A3215 MG. %I A3261 N1842.5 %S A3261 1,7,23,63,159,383,895,2047,4607,10239,22527,49151,106495,229375, %T A3261 491519,1048575,2228223,4718591,9961471,20971519,44040191,92274687 %N A3261 WOODALL NUMBERS N.2**N - 1. %R A3261 BR2 159. %I A3148 N1846.5 %S A3148 1,7,27,321,2265,37575,390915,8281665,114610545,2946939975, %T A3148 51083368875,1542234996225,32192256321225,1114841223671175 %N A3148 A(N+1) = A(N) + 2N(2N+1)A(N-1). %R A3148 FQ 10 171 72. %C N1866 N1866 %N N1866 C(2N,N-3).7/(N+4). %R N1866 QAM 14 407 56. MTAC 29 216,75。VEH1. %I A3516 N1866.3 %S A3516 1,7,36,165,715,3003,12376,50388,203490,817190,3268760,13037895, %T A3516 51895935,206253075,818809200,3247943160,12875774670,51021117810 %N A3516 BINOMIAL COEFFICIENTS C(2N+1,N-2). %R A3516 AS1 828. %I A3418 N1866.5 %S A3418 1,7,37,58,163,4687,30178,30493,47338 %N A3418 EXTREME VALUES OF DIRICHLET SERIES. %R A3418 PSPM 24 277 73. %I A3464 N1870.5 %S A3464 1,7,43,259,1555,9331,55987,335923,2015539,12093235,72559411, %T A3464 435356467,2612138803,15672832819,94036996915,564221981491,3385331888947 %N A3464 (6**N - 1)/5. %R A3464 %I A3286 N1877.5 %S A3286 1,7,66,916,16816 %N A3286 SEMI-REGULAR DIGRAPHS. %R A3286 KNAW 75 330 72. %C N1893 N1893 %S N1893 1,7,791,3748629,151648960887729,1323497544567561138595307148089 %N N1893 AN EXPANSION FOR PI. %R N1893 AMM 54 138 47. {AW8080N1894.5%S S A29 80,1,8,0,24,0560,029 76,016464,094016,054 9648 327 3040,% %T A29 80 1978116812 10209607808039 55 2 2 %的正方形晶格上的A29 80 SelfooIdIn环。%R A29 80 JCP 34 1532 61。PHYSA 5 66572. %I A2994 N1895.5 %S A2994 1,8,2,6,1,2,3,5,7,1,1,1,2,2,3,4,4,5,6,8,9,1,1,1,1,1,1,2,2,2,2,3,3, %T A2994 3,4,4,5,5,5,6,6,7,7,8,9,9,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3 %N A2994 INITIAL DIGITS OF CUBES. %R A2994 %I A3056 N1899.5 %S A3056 1,8,17,20,21,24,112,113,116,119,122,125,128,131,144,145,171,179, %T A3056 182,183,209,217,238,262,268,276,279,282,308,311,324,340,351,354,375,383 %N A3056 RELATED TO THE N GOES TO N/2 (IF EVEN) OR 3N+1 (IF ODD) PROBLEM. %R A3056 PC11 1-3 73. %I A3249 N1900.5 %S A3249 1,8,21,29,42,50,55,63,76,84,97,110,118,131,139,144,152,164,173,186, %T A3249 194,199,207,220,228,241,254,262,275,283,288,296,309,317,330,338,343,351 %N A3249 RELATED TO FIBONACCI REPRESENTATIONS. %R A3249 FQ 11 385 73. %I A2968 N1901.5 %S A2968 1,8,22,51,342,2609,16896,99114 %N A2968 A QUEEN-PLACING PROBLEM. %R A2968 SIAMR 14 173 72. AcA 23 117 117,73μ.c N193 N193 NS3,N193,1,8,2411256061641694091696648 1978116878080955,2 %N,N803,在正方点阵上,N%RN33JCP 34 1532 61。PHYSA 5 66572. %I A3201 N1908.5 %S A3201 1,8,32,108,348,1068,3180,9216 %N A3201 CLUSTER SERIES FOR SQUARE LATTICE. %R A3201 PRV 133 A315 64. %C N1915 N1915 %S N1915 1,8,36,229,1625,13208,120288,1214673,13469897,162744944,2128047988, %T N1915 29943053061,451123462673,7245940789072,123604151490592,2231697509543361 %N N1915 A(N+2) = (N-1)A(N+1) + 2NA(N) + NA(N-1). %R N1915 PLMS 31 341 30. SPS 34-40-4209 66 .19%19N1916,N1916,N1916,1,8,40160917625635460244224024122464,475,7621863680,% T N1916 45 875 201114112086686635043144942208033565 20208074035200%N N1916C(n,3).2 **(n-3).% %R N1916 PRSE 62 190 46。AS1 796。MFM 74 62×70 .19%C N1919N1919%N1919的非三线问题。WE1 124。CM2 7. %I A3518 N1919.3 %S A3518 1,8,44,208,910,3808,15504,62016,245157,961400,3749460,14567280, %T A3518 56448210,218349120,843621600,3257112960,12570420330,48507033744 %N A3518 C(2N+1,N-3).8/(N+5). %R A3518 VEH1. %I A3220 N1919.5 %S A3220 1,8,44,208,984,4584,21314,98292,448850,2038968,9220346,41545564, %T A3220 186796388,838623100 %N A3220 SUSCEPTIBILITY FOR DIAMOND LATTICE. %R A3220 PHYSA 6 1511 73. %C N1921 N1921 %S N1921 1,8,45,220,1001,4368,18564,77520,319770,1307504,5311735,21474180, %T N1921 86493225,347373600,1391975640,5567902560,22239974430,88732378800 %N N1921 BINOMIAL COEFFICIENTS C(2N,N-3). %R N1921 LA4 517. As1 828 .i %A1910 N1927.5%S S A32 101,8,56248123256902663611355 2π%A310立方晶格系列,%R R A32 10 PRV 133 A315 64。DG2 225. %I A3494 N1927.7 %S A3494 1,8,56,384,2536,16512,105664,669696,4201832,26183808,162073408, %T A3494 998129664,6117389760,37346353152,227164816896,1377490599936 %N A3494 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3494 DG2 404. %C N1928 N1928 %S N1928 1,8,56,392,2648,17864,118760,789032,5201048,34268104,224679864, %T N1928 1472595144,9619740648,62823141192,409297617672,2665987056200 %N N1928 SUSCEPTIBILITY FOR CUBIC LATTICE. %R N1928 PHYSA 5 651 72. %C N1929 N1929 %N N1929 WALKS ON A CUBIC LATTICE. %R N1929 PHYSA 5 659 72. %C N1935 N1935 %S N1935 1,8,61,5020,12854155,162924332716605980, %T N1935 28783052231699298507846309644849796 %N N1935 AN EXPANSION FOR PI. %R N1935 AMM 54 138 47. JWW. %C N1942 N1942 %N N1942 EVERY SEQ OF 2 NUMBERS > A(N) CONTAINS A PRIME > P(N). %R N1942 IJM 8 66 64.AMM 79 1087 72. %I A3492 N1942.3 %S A3492 1,8,88,840,6888,54824,412712,3065096,22134152 %N A3492 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3492 DG2 136. %I A3497 N1942.7 %S A3497 1,8,88,1216,19160,327232,5896896,110393856,2126213592,41861519680, %T A3497 838733719616 %N A3497 INTERNAL ENERGY SERIES FOR CUBIC LATTICE. %R A3497 DG2 425. %C N1945 N1945 %S N1945 1,8,104,1092,12376,136136,1514513,16776144,186135312,2063912136, %T N1945 22890661872,253854868176,2815321003313,31222272414424,34620798314872 %N N1945 FIBONOMIAL COEFFICIENTS. %R N1945 FQ 6 82 68. BR1 74. %I A3491 N1950.5 %S A3491 1,8,152,2200,28520,347416,4068024,46360392 %N A3491 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3491 DG2 136. %I A3435 N1951.5 %S A3435 1,8,192,11904,1125120,153262080,28507207680,6951513784320, %T A3435 2153151603671040,826060810479206400,384600188992919961600 %N A3435 HAMILTONIAN CIRCUITS ON N-OCTAHEDRON. %R A3435 SI4. %I A3297 N1978.5 %S A3297 1,9,49,214,800,2685,8274,23829,64843 %N A3297 COEFFICIENTS OF A MODULAR FUNCTION. %R A3297 GMJ 8 29 67. %C N1981 N1981 %N N1981 C(2N,N-4).9/(N+5). %R N1981 QAM 14 407 56. MTAC 29 216,75。Nave1.0%C N1982 1982年1月9日,第569期,第212952285期,第2期,第2期,第2期,第2期,1982年,第13期,第2期,1982年,第2期,第2期,1982年,第13期,第2期。REA1. %I A3408 N1985.5 %S A3408 1,9,66,455,3060,20349,134596,888030 %N A3408 CONNECTED LADDER GRAPHS. %R A3408 DM 9 355 74. %C A2051 N1986 %S A2051 1,9,67,525,4651,47229,545707,7087005,102247051,1622631549, %T A2051 28091565547,526858344285,10641342962251,230283190961469,5315654681948587 %N A2051 A SUM INVOLVING STIRLING NUMBERS. %R A2051 SKA 11 95 28. %I A3302 N1993.5 %S A3302 1,9,81,8505,229635,413343,531972441,227988189,3419822835 %N A3302 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3302 RS3 273 593 73. %I A3280 N1996.2 %S A3280 1,9,175,2025,102235,1356047,37160123,6771931925,772428184055 %N A3280 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3280 RS3 273 590 73. %I A3026 N1996.5 %S A3026 1,9,198,10710,1384335,416990763,286992935964,444374705175516, %T A3026 1528973599758889005 %N A3026 ACYCLIC DIGRAPHS WITH 2 OUT-POINTS. %R A3026 HA7 254. %C N1997 N1997 %N N1997 (1.3.5...(2N-1))**2. %R N1997 RCI 217. %I A3303 N1998.5 %S A3303 1,9,297,7587,1086939,51064263,5995159677,423959714955, %T A3303 281014370213715,26702465299878195,5723872792950096855 %N A3303 SPIN-WAVE COEFFICIENTS FOR CUBIC LATTICE. %R A3303 RS3 273 605 73. %I A3133 N2000.5 %S A3133 1,10,2,16,2,1,4,2,1,21,1,3,5,1,2,1,1,2,11,5,1,3,1,2,27,4,1,282,8,1, %T A3133 2,1,1,3,1,3,2,6,4,1,2,1,5,1,1,2,1,1,1,3,2,8,1,2,2,4,5,1,1,36,1,1,1,1,2 %N A3133 CONTINUED FRACTION EXPANSION OF CUBE ROOT OF 7. %R A3133 JRAM 255 126 72. %I A3001 N2002.5 %S A3001 1,10,25,39,77,679,6788,68889,2677889,26888999,3778888999, %T A3001 277777788888899 %N A3001 SMALLEST NUMBER OF PERSISTENCE N. %R A3001 JRM 6 97 73. %I A3012 N2003.5 %S A3012 1,10,33,81,148 %N A3012 PACKING 2-CUBES IN A TORUS. %R A3012 SIAMP 4 98 71. %I A3197 N2010.5 %S A3197 1,10,46,186,706,2568,9004,30894,103832,343006 %N A3197 CLUSTER SERIES FOR TRIANGULAR LATTICE. %R A3197 PRV 133 A315 64. DG2 225π.I A37N2015%S S A370 1,10,5023 811 14499 8225629 844 1744 39941855 356 6 %N 7A7 7系列立方晶格系列,%R R A37 PRV 133 A315 64。DG2,225,I,A372,N2015.5,S A34 72,1,10,6028011204240424024126067,80250242427 955 20,% T A34 72 754 7969606605013407127870171721919 207844 65 9202019175833 60 %,n A34 72 C(n,4)。2×*(n 4)。AS1 796. %I A3519 N2017.5 %S A3519 1,10,65,350,1700,7752,33915,144210,600875,2466750,10015005, %T A3519 40320150,161280600,641886000,2544619500,10056336264,39645171810 %N A3519 C(2N+1,N-4).10/(N+6). %R A3519 VEH1. %C N2025 N2025 %S N2025 1,10,91,820,7381,66430,597871,5380840,48427561,435848050, %T N2025 3922632451,35303692060,317733228541,2859599056870,25736391511831 %N N2025 (9**N - 1)/8. %R N2025 TH1 36. FMR 1 112。RCI 217 .%C.A1762N29 29 N%A1762球的解剖。% %R A1762 CMA 2 25 25。MAN 191 98 71. %I A2967 N2030.5 %S A2967 1,10,215,12231,2025462 %N A2967 REPRESENTATIONS OF 1 AS A SUM OF UNIT FRACTIONS. %R A2967 SI3. %C A0459 N2032 %S A0459 1,10,297,13756,925705,85394646,10351036465,1596005408152, %T A0459 305104214112561,70830194649795010,19629681235869138841 %N A0459 PERMUTATIONS WITH NO HITS ON 2 MAIN DIAGONALS. %R A0459 R1 187. %I A3284 N2038.5 %S A3284 1,11,19,7861,301259,451526509,6427914623,16794274237 %N A3284 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3284 RS3 273 593 73. %C N2048 N2048 %N N2048 C(2N,N-5).11/(N+6). %R N2048 QAM 14 407 56. MTAC 29 216,75。VEH1. %I A3021 N2050.5 %S A3021 1,11,101,13,137,9091,9901,909091,5882353,52579,27961,8779,99990001, %T A3021 1058313049,121499449,9091,69857,21993833369,999999000001 %N A3021 LARGEST FACTOR OF 100...01. %R A3021 KR2 40. %C N2064 N2064 %S N2064 1,12,14,135,276,1520,4056,17778,54392,213522,700362,2601674, %T N2064 8836812,31925046,110323056,393008712,1369533048 %N N2064 SUSCEPTIBILITY FOR CUBIC LATTICE. %R N2064 PHYSA 6 1511 73. %C N2065 N2065 %S N2065 1,12,24,60,180,588,1968,6840,24240,87252,318360,1173744,4366740, %T N2065 16370700,61780320,234505140,894692736 %N N2065 SELFAVOIDING RINGS ON A TRIANGULAR LATTICE. %R N2065 PHYSA 5 665 72. %I A3498 N2067.5 %S A3498 1,12,48,252,1440,8544,52416,330588,2130240,13961808,92784384, %T A3498 623772288,4234688640,28990262016,199908428544,1387276513308 %N A3498 INTERNAL ENERGY SERIES FOR CUBIC LATTICE. %R A3498 DG2 425. %I A3200 N2072.5 %S A3200 1,12,66,312,1368,5685 %N A3200 CLUSTER SERIES FOR HONEYCOMB. %R A3200 PRV 133 A315 64. %IA399N2074.5s%A391.1,1284504301217142%N A39簇立方晶格系列,%R R A39PRV 133 A315 64。DG2 225. %I A3431 N2075.5 %S A3431 1,12,104,956 %N A3431 IRREDUCIBLE POSETS. %R A3431 PAMS 45 298 74. %I A3495 N2080.5 %S A3495 1,12,132,1392,14292,144000,1430592,14057280,136914804,1323843936, %T A3495 12722294736,121625850240,1157512059936,10972654675200,103654156958208 %N A3495 SUSCEPTIBILITY FOR CUBIC LATTICE. %R A3495 DG2 404. %C N2081 N2081 %N N2081 SUSCEPTIBILITY OF CUBIC LATTICE. %R N2081 SSP 3 268 70. PHYSA 5 651 72. %I A3130 N2086.5 %S A3130 1,12,157,1750,17446,164108,1505099,13720902,125782441 %N A3130 IMPEDANCES OF AN N-TERMINAL NETWORK. %R A3130 BSTJ 18 301 39. %I A3154 N2096.5 %S A3154 1,13,37,73,121,181,253,337,433,541,661,793,937,1093,1261,1441,1633, %T A3154 1837,2053,2281,2521,2773,3037,3313,3601,3901,4213,4537,4873,5221,5581 %N A3154 STAR NUMBERS 6N(N+1) + 1. %R A3154 MG. %C A1662 N2098 %S A1662 1,13,47,73,2447,16811,15551,1726511,18994849,10979677,2983409137, %T A1662 48421103257,135002366063,10125320047141,232033147779359,1305952009204319 %N A1662 COEFFICIENTS OF AIREY'S CONVERGING FACTOR. %R A1662 KNAW 66 751 63. PNAS 69440 72,ε%C N2104 N2104%N N2104C(2N,N-6)13(/ N+6).% %R N2104 QAM 14 407 56。MTAC 29 216,75。We 1.21C N2112 N2112 S N2112、1327 34、185085 15145、1327、2627、1234、48、885、608、1948、77、1626、588、T N2112、15737、370、370、28、135、40845、850675、8080596990338、68、407700、99、%、N、N2112的模糊系数。A983N2112.5,%S S A29 81,1,14,14,21,35,32,30,95,24,20,96,7,85,6,9,6,9,18,37,7,37,76,37,97,37,99,7,37,7,32,47,84,62,10,70,38,85,3,8,53,53,43,27,%,N,A29,74对2的平方根。BR1 74。MTAC 22 899 899。dg2,n.21c n2115,n2115,%s,n2115,141482525528028 1485 1275 582037 306501797 818088877 60,% %t n2115 395482815 n%n2115多个部分的多边形的剖分。REA1. %I A2961 N2120.5 %S A2961 1,14,206,957,1334,1364,1634,2685,2974,4364 %N A2961 N AND N+1 HAVE SAME SUM OF DIVISORS. %R A2961 SI2 110. %C N2151 N2151 %S N2151 1,16,18,0,252,576,519,3264,12468,20568,26662,215568,528576,164616, %T N2151 3014889,10894920,13796840,29909616,190423962,399739840,22768752 %N N2151 SUSCEPTIBILITY FOR CUBIC LATTICE. %R N2151 PHYSA 6 1511 73. %I A3109 N2179.5 %S A3109 1,17,117,1413,46389,1211085 %N A3109 SPECIAL PERMUTATIONS. %R A3109 JNT 5 48 73. %I A3300 N2185.5 %S A3300 1,18,24,27216,5878656,105815808,346652587008,693305174016 %N A3300 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3300 RS3 273 593 73. %I A3298 N2192.2 %S A3298 1,18,648,2160,1399680,75582720,149653785600,2693768140800, %T A3298 8620058050560 %N A3298 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3298 RS3 273 593 73. %I A3030 N2192.5 %S A3030 1,18,1606,565080,734774776,3520944131920,63569709615130544 %N A3030 STRONGLY CONNECTED DIGRAPHS. %R A3030 HA7 270. %IA35N2220.5%S S.A355,1,2223 4262262621464 2192,133立方晶系,n %R A355 PRV,A315 64。DG2 225. %I A3468 N2220.8 %S A3468 1,22,305,3410,33621,305382,2619625,21554170,171870941,1337764142, %T A3468 10216988145,76862115330,571247591461,4203844925302,30687029023865 %N A3468 MINIMAL COVERS. %R A3468 DM 5 249 73. %I A3281 N2227.5 %S A3281 1,23,1477,555273,38466649,1711814393,48275151899,28127429172349 %N A3281 COEFFICIENTS OF GREEN FUNCTION FOR CUBIC LATTICE. %R A3281 RS3 273 590 73. %C N2230 N2230 %S N2230 1,24,26,0,0,72,378,1080,665,384,1968,2016,25698,39552,3872,20880, %T N2230 65727,379072,1277646,986856,176978,2163504,1818996,27871080,47138844 %N N2230 SUSCEPTIBILITY FOR CUBIC LATTICE. %R N2230 PHYSA 6 1510 73. %C N2238 N2238 %S N2238 1,24,264,3312,48240,762096,12673920,218904768,3891176352 %N N2238 SELFAVOIDING RINGS ON A CUBIC LATTICE. %R N2238 JCP 34 1537 61. PHYSA 5 66572. %I A3170 N2245.5 %S A3170 1,24,1344,393120,155185920,143432634240 %N A3170 4-LINE LATIN RECTANGLES. %R A3170 FQ 11 246 73. %I A3164 N2292.5 %S A3164 1,37,111,177,177,2753,2753,827,827,8386459,8386459,28033727, %T A3164 28033727,14529522883,14529522883,1799010587,1799010587,47497385017 %N A3164 NUMERATORS OF VAN DER POL NUMBERS. %R A3164 JRAM 260 35 73. %I A3020 N2292.8 %S A3020 1,37,271,4649,333667,513239,265371653,2906161,5363222357, %T A3020 1111111111111111111,10838689,11111111111111111111111,182521213001 %N A3020 LARGEST FACTOR OF 11...1 (ODD NUMBER OF 1'S). %R A3020 KR2 40. %I A2975 N2323.5 %S A2975 1,70,836,4030,5830,7192,7912,9272,10792,17272,45356,73616,83312, %T A2975 91388,113072,243892,254012,338572,343876,388076,519712,539774,555616 %N A2975 PRIMITIVE WEIRD NUMBERS. %R A2975 AMM 79 774 72. MTAC 28 618 74. %C N2330 N2330 %S N2330 1,96,1776,43776,1237920,37903776,1223681760,41040797376 %N N2330 SELFAVOIDING RINGS ON A CUBIC LATTICE. %R N2330 PHYSA 5 665 72. %I A2952 N2332.5 %S A2952 1,114,1140,18018,32130,44772,56430,67158,142310,180180,197340, %T A2952 241110,296010,308220,462330,591030,669900,671580,785148,815100 %N A2952 UNITARY AMICABLE NUMBERS. %R A2952 MTAC 25 917 71. %I A3015 N2332.8 %S A3015 1,120,210,1540,3003,7140,11628,24310 %N A3015 COINCIDENCES AMONG BINOMIAL COEFFICIENTS. %R A3015 AMM 78 1119 71. %I A3438 N2337.5 %S A3438 1,120,6210,153040,2224955,22069251,164176640,976395820,4855258305, %T A3438 20856798285,79315936751 %N A3438 5X5 STOCHASTIC MATRICES OF INTEGERS. %R A3438 JVR1. %I A2953 N2340.5 %S A2953 1,126,1260,22302,40446,49308,64530,73962,168730,223020,286500, %T A2953 242730,429750,365700,548550,618570,827700,739620,827652,932100 %N A2953 UNITARY AMICABLE NUMBERS. %R A2953 MTAC 25 917 71. %I A3321 N2348.5 %S A3321 1,153,1634,4150,548834,3077 74πn A33 21最小数等于其数字的n次方之和。17417252467 80501465 112084671 48。SI1 215。MTAC 25 944 71. %I A3294 N2368.2 %S A3294 1,353,651,2487,2501,2829,3723,3973,4267,4333,4449,4949,5281,5463, %T A3294 5491,5543,5729,6167,6609,6801,7101,7209,7339,7703,8373,8433,8493,8517 %N A3294 4-TH POWER OF N = SUM OF 4 4-TH POWERS. %R A3294 MTAC 27 492 73. %I A2997 N2365.5 %S A3294 1,561,1105,1729,2465,2821,6601,8911,10585,15841,29341,41041,46657, %T A3294 52633,62745,63973,75361,101101,115921,126217,162401,172081,188461,252601 %N A3294 CARMICHAEL NUMBERS. %R A3294 SPH 8 45 38. Si2 51。MTAC 25 944 944。