This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063489 #31 Dec 20 2024 12:39:07
%S A063489 1,8,30,77,159,286,468,715,1037,1444,1946,2553,3275,4122,5104,6231,
%T A063489 7513,8960,10582,12389,14391,16598,19020,21667,24549,27676,31058,
%U A063489 34705,38627,42834,47336,52143,57265,62712,68494,74621,81103,87950,95172,102779,110781,119188
%N A063489 a(n) = (2*n-1)*(5*n^2-5*n+6)/6.
%H A063489 Harry J. Smith, <a href="/A063489/b063489.txt">Table of n, a(n) for n = 1..1000</a>
%H A063489 T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Rep., 273 (1996), 199-241, eq. (10).
%H A063489 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A063489 G.f.: x*(1+x)*(1+3*x+x^2)/(1-x)^4. - _Colin Barker_, Mar 02 2012
%F A063489 a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), with a(1)=1, a(2)=8, a(3)=30, a(4)=77. - _Harvey P. Dale_, Aug 20 2012
%F A063489 E.g.f.: (-6 + 12*x + 15*x^2 + 10*x^3)*exp(x)/6 + 1. - _G. C. Greubel_, Dec 01 2017
%t A063489 Table[(2n-1)(5n^2-5n+6)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,8,30,77},40] (* _Harvey P. Dale_, Aug 20 2012 *)
%o A063489 (PARI) a(n) = { (2*n - 1)*(5*n^2 - 5*n + 6)/6 } \\ _Harry J. Smith_, Aug 23 2009
%o A063489 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-6 + 12*x + 15*x^2 + 10*x^3 )*exp(x)/6 + 1)) \\ _G. C. Greubel_, Dec 01 2017
%o A063489 (Magma) [(2*n-1)*(5*n^2-5*n+6)/6: n in [1..30]]; // _G. C. Greubel_, Dec 01 2017
%Y A063489 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 A063489 Partial sums of A010001.
%Y A063489 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. See the Proserpio link in A299266 for overview.
%K A063489 nonn,easy
%O A063489 1,2
%A A063489 _N. J. A. Sloane_, Aug 01 2001