来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a005902 Showing 1-1 of 1 %I A005902 M4898 %S A005902 1,13,55,147,309,561,923,1415,2057,2869,3871,5083,6525,8217,10179, %T A005902 12431,14993,17885,21127,24739,28741,33153,37995,43287,49049,55301, %U A005902 62063,69355,77197,85609,94611,104223,114465,125357,136919,149171 %N A005902 Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice. %C A005902 Called "magic numbers" in some chemical contexts. %C A005902 Partial sums of A005901(n). - 10月30日LekRaj-Bead SysIa,2003×%C A000 5902等于1, 12, 30,20, 0, 0,0,……的二项变换。- Ag3晶格的Ag 01,2008μ%C A000 5902晶体球序列。-迈克尔索莫斯,Jun 03 2012 A.0%D A000 5902 H.S.M.Cox,多面体数,25.35,R. S. Cohen,J. J. Stachel和M. W. Wartofsky,EDS。Dirk Struik:科学,历史和政治论文,纪念Dirk J. Struik,Reidel,多德雷赫特,1974。n,a(n)n=0…1000的表%H A00 5902 S. Bjornholm,团簇,胚胎中的凝聚物质沉思。Phys。31 1990 pp.309 324.0%H A00 5902 J. H. Conway和N.J.A.斯隆,低维格子VII:协调序列,PROC。皇家SOC伦敦,A453(1997),369-2489.PDFNicolas Gastineau,Olivier Togni,面心立方网格的d次幂着色,ARXIV:1806.08136 [C.DM],2018 .%%HA55902 D. R. Herrick,主页(将这些数字显示为化学中的簇大小):%HA55902 T. P. Martin,原子壳层Phys。报告,273(1996),19-241,等式(11).%%H A00 5902 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B. K. Teo大学和新泽西州大学,1992。多边形和多面体簇中的幻数Inorgan。化学。24(1985),445~45.58立方八面体球填料%H A00 5902水晶球序列索引条目%H A00 5902与F.C.C.晶格相关的序列的索引条目%H A00 5902常系数线性递归的索引项签名(4,-6,4,- 1).{%A00 5902 A(n)=(2×n+1)*(5×n ^ 2+5×n+3)/3 .% f f a00 5902为n> 0,n*a(n)=(SuMu{{i=0…n-1 } A(i))+ 2*a00 5891(n)*a000 0217(n)。-Bruno BelSeliz,FEB 02 2011μF F A00 5902 A(- 1 -N)=-A(n)。- _Michael Somos_, Jun 03 2012 %F A005902 From _Indranil Ghosh_, Apr 08 2017: (Start) %F A005902 G.f.: (x^3 + 9x^2 + 9x + 1)/(x - 1)^4. %F A005902 E.g.f.: (1/3)*exp(x)*(10x^3 + 45x^2 + 36x + 3). %F A005902 (End) %F A005902 a(n) = A100171(n+1) - A008778(n-1) = A100174(n+1) - A000290(n) = A005917(n+1) - A006331(n) = A051673(n+1) + A000578(n). -Brice J.尼科松,JUL 05(2018)%E A00 5902 A(4)=147=(1, 3, 3,1)点(1, 12, 30,20)=(1+36+90+20)。- _Gary W. Adamson_, Aug 01 2008 %e A005902 G.f. = 1 + 13*x + 55*x^2 + 147*x^3 + 309*x^4 + 561*x^5 + 923*x^6 + 1415*x^7 + ... %p A005902 A005902 := n -> (2*n+1)*(5*n^2+5*n+3)/3; %p A005902 A005902:=(z+1)*(z**2+8*z+1)/(z-1)**4; # _Simon Plouffe_ in his 1992 dissertation %t A005902 f[n_] := (2n + 1)(5n^2 + 5n + 3)/3; Array[f, 36, 0] (* _Robert G. Wilson v_, Feb 02 2011 *) %t A005902 LinearRecurrence[{4,-6,4,-1},{1,13,55,147},50] (* _Harvey P. Dale_, Oct 08 2015 *) %t A005902 CoefficientList[Series[(x^3 + 9*x^2 + 9*x + 1)/(x - 1)^4, {x, 0, 50}], x] (* _Indranil Ghosh_, Apr 08 2017 *) %o A005902 (PARI) {a(n) = (2*n + 1) * (5*n^2 + 5*n + 3) / 3}; /* _Michael Somos_, Jun 03 2012 */ %o A005902 (PARI) x='x+O('x^50); Vec((x^3 + 9*x^2 + 9*x + 1)/(x - 1)^4) \\ _Indranil Ghosh_, Apr 08 2017 %o A005902 (MAGMA) [(2*n+1)*(5*n^2+5*n+3)/3: n in [0..30]]; // _G. C. Greubel_, Dec 01 2017 %Y A005902 (1/12)*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496. %Y A005902 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。%AY55902 CF.A100171,A100174,A051673.0%K A000 5902非n,易,很好,%AO A00 5902 0,2 %,AO55902,N.J.A.SLaNeNexi的内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/许可证