来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a309694 Showing 1-1 of 1 %I A309694 %S A309694 0,0,0,0,2,2,6,4,14,14,28,24,48,44,74,68,112,106,158,144,214,206,286, %T A309694 268,370,352,466,444,584,562,716,680,864,838,1038,996,1230,1188,1440, %U A309694 1392,1682,1634,1944,1876,2228,2174,2548,2472,2892,2816,3260,3176,3670 %N A309694 Sum of the even parts appearing among the largest parts of the partitions of n into 3 parts. %H A309694 Colin Barker,n,a(n)n=0…1000的表%H A309692与分区相关的序列的索引条目%H A309692常系数线性递归的索引项, signature (1,-1,1,1,-1,3,-3,2,-2,-2,2,-3,3,-1,1,1,-1,1,-1). %F A309694 a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (n-i-j) * ((n-i-j-1) mod 2). %F A309694 From _Colin Barker_, Aug 23 2019: (Start) %F A309694 G.f.: 2*x^4*(1 + 3*x^2 - x^3 + 6*x^4 - x^5 + 7*x^6 - x^7 + 6*x^8 - x^9 + 3*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)^2*(1 + x^2)^2*(1 + x + x^2)^2). %F A309694 a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + 3*a(n-6) - 3*a(n-7) + 2*a(n-8) - 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14) + a(n-15) + a(n-16) - a(n-17) + a(n-18) - a(n-19) for n>18. %F A309694 (End) %e A309694 Figure 1: The partitions of n into 3 parts for n = 3, 4, ... %e A309694 1+1+8 %e A309694 1+1+7 1+2+7 %e A309694 1+2+6 1+3+6 %e A309694 1+1+6 1+3+5 1+4+5 %e A309694 1+1+5 1+2+5 1+4+4 2+2+6 %e A309694 1+1+4 1+2+4 1+3+4 2+2+5 2+3+5 %e A309694 1+1+3 1+2+3 1+3+3 2+2+4 2+3+4 2+4+4 %e A309694 1+1+1 1+1+2 1+2+2 2+2+2 2+2+3 2+3+3 3+3+3 3+3+4 ... %e A309694 ----------------------------------------------------------------------- %e A309694 n | 3 4 5 6 7 8 9 10 ... %e A309694 ----------------------------------------------------------------------- %e A309694 a(n) | 0 2 2 6 4 14 14 28 ... %e A309694 ----------------------------------------------------------------------- %t A309694 Table[Sum[Sum[(n - i - j) * Mod[n - i - j - 1, 2], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}] %t A309694 LinearRecurrence[{1, -1, 1, 1, -1, 3, -3, 2, -2, -2, 2, -3, 3, -1, 1, 1, -1, 1, -1}, {0, 0, 0, 0, 2, 2, 6, 4, 14, 14, 28, 24, 48, 44, 74, 68, 112, 106, 158}, 80] %o A309694 (PARI) concat([0,0,0,0], Vec(2*x^4*(1 + 3*x^2 - x^3 + 6*x^4 - x^5 + 7*x^6 - x^7 + 6*x^8 - x^9 + 3*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)^2*(1 + x^2)^2*(1 + x + x^2)^2) + O(x^40))) \\ _Colin Barker_, Aug 23 2019 %Y A309694 Cf. A026923, A026927, A309683, A309684, A309685, A309686, A309687, A309688, A309689, A309690, A309692. %K A309694 nonn,easy %O A309694 0,5 %A A309694 _Wesley Ivan Hurt_, Aug 12 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE