来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a005897 Showing 1-1 of 1 %I A005897 M4497 %S A005897 1,8,26,56,98,152,218,296,386,488,602,728,866,1016,1178,1352,1538, %T A005897 1736,1946,2168,2402,2648,2906,3176,3458,3752,4058,4376,4706,5048, %U A005897 5402,5768,6146,6536,6938,7352,7778,8216,8666,9128,9602,10088,10586 %N A005897 a(n) = 6*n^2 + 2 for n > 0, a(0)=1. %C A005897 Number of points on surface of 3-dimensional cube in which each face has a square grid of dots drawn on it (with n+1 points along each edge, including the corners). %C A005897 Coordination sequence for b.c.c. lattice. %C A005897 Also coordination sequence for 3D uniform tiling with tile an equilateral triangular prism. ---J.A.SLaNeNez,FEB 06(2018,%C)A00 5897二项变换的[ 1, 7, 11,1,-1, 1,-1, 1,…]。10月22日,2007 C%A00 5897中心立方体数(A00 5898)的第一个差异:n^ 3+(n+1)^ 3。-JoaaWay-VoS PASTY,FEB 06 2011πC A00 5897除了第一项,形式(R^ 2+2×s^ 2)* n ^ 2+2=(R*n)^ 2 +(S*N-1)^ 2 +(S*N+1)^ 2:在这种情况下是r= 2,s= 1。8后,所有条款均为A000 0408。-Bruno BelSeliz,FEB 07,2012πC A00 5897,n>0,最后一个数字序列(即A(n)mod 10)是(8, 6, 6,8, 2)永远重复。-μ.F.HasLeLyr,APR 05,2016μ%C.A00 5897,边缘长度为1的立方体的数量,需要一个边缘长度为n+1的空心立方体。-彼得M. CeaMay,APR 01 2017μ%D A000 5897 H.S.M.科克斯特,“多面体数”,在R.S.科恩等人,编辑,Dirk Struik。雷德尔,多德雷赫特,1974,pp.25-35.0%D A000 5897 GMELIN手册的iNORG。有机溶剂。化学,第八ED,1994,TyPIX搜索代码(194)HP4*%D A000 5897 B Gr u NbAUM,3-空间的均匀倾斜,GEOMIN,4(1994),49-56。请参阅TILLY 11,R. W. Marks,R. B. Fuller,Ad58897,Buckminster Fuller的DyMax世界。抛锚,NY,1973,第46页.0%D A000 5897 N.J.A.斯隆和Simon Plouffe,整数序列百科全书,学术出版社,1995(包括这个序列).21%A00 58897 B. K. Teo和N.J.A.斯隆,多边形和多面体团中的幻数,Inorgan。化学。24(1985),445~45.58n,a(n)n=0…10000的表%H A00 5897 R.W GROSE KunStLeVe,协调序列与整数序列百科全书%H A00 5897 R.W GROSE KunSTLeVe,G. O. Brunner和N.J.A.斯隆,分子筛的配位序列和精确拓扑密度的代数描述,Acta Cryst,A52(1996),pp.899—88. %H HA55897 Simon Plouffe,近似逼近学位论文,博士论文,Simon Plouffe大学,19921031生成函数与猜想,大学校区,1992。格的协调序列Zeit。F.Kistar,210(1995),905-908。[注释扫描的副本] %%AA55897网状化学结构资源(RCSR),六角瓷砖(或网)%H A00 5897与B.C.C.晶格相关的序列的索引条目%H A00 5897常系数线性递归的索引项,签名(3,-3,1).% %F A00 5897 G.F.:(1 + x)*(1 + 4×x+x^ 2)/(1-x)^ 3。- Sim-Simon Pouffeef.%f f A00 5897 A(0)=1,A(n)=(n+1)^ 3(n-1)^ 3。- Ilya Nikulshin(ILYNIIK(AT)Gmail),8月11日,2009μF F A00 5897 A(0)=1,A(1)=8,A(2)=26,A(3)=56;对于n>3,A(n)=3*a(n-1)-3*a(n-2)+a(n-3)。10月25日,2011岁的F·A00 5897 A(n)=A033581+(2)。4月27日,2014岁F F A00 5897 E.G.F.:2*(1 + 3×X + 3×X ^ 2)*EXP(X)-1。- _G. C. Greubel_, Dec 01 2017 %e A005897 For n = 1 we get the 8 corners of the cube; for n = 2 each face has 9 points, for a total of 8 + 12 + 6 = 26. %p A005897 A005897:=-(z+1)*(z**2+4*z+1)/(z-1)**3; # conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation %t A005897 Join[{1},6Range[50]^2+2] (* or *) Join[{1},LinearRecurrence[{3,-3,1},{8,26,56},50]] (* _Harvey P. Dale_, Oct 25 2011 *) %o A005897 (MAGMA) [1] cat [6*n^2 + 2: n in [1..50]]; // _Vincenzo Librandi_, Oct 26 2011 %o A005897 (PARI) a(n)=if(n,6*n^2+2,1) \\ _Charles R Greathouse IV_, Mar 06 2014 %o A005897 (PARI) x='x+O('x^30); Vec(serlaplace(2*(1 + 3*x + 3*x^2)*exp(x) - 1)) \\ _G. C. Greubel_, Dec 01 2017 %o A005897 (Haskell) a005897 n = if n == 0 then 1 else 6 * n ^ 2 + 2 -- _Reinhard Zumkeller_, Apr 27 2014 %Y A005897 Cf. A000578, A206399. %Y A005897 See A005898 for partial sums. %Y A005897 The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. 参见A29 9266中的Pro SeriPIO链路。%KN A00 5897非n,易,很好,%AO A00 5897 0,2 %,AO58897,N.J.A.SLaNeNe],γ-Ralf W.GROSESE-KunStLeVeVi]内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/许可证