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 A063495 #25 Dec 20 2024 12:40:54
%S A063495 1,18,80,217,459,836,1378,2115,3077,4294,5796,7613,9775,12312,15254,
%T A063495 18631,22473,26810,31672,37089,43091,49708,56970,64907,73549,82926,
%U A063495 93068,104005,115767,128384,141886,156303,171665,188002,205344,223721,243163,263700,285362
%N A063495 a(n) = (2*n-1)*(5*n^2-5*n+2)/2.
%H A063495 Harry J. Smith, <a href="/A063495/b063495.txt">Table of n, a(n) for n = 1..1000</a>
%H A063495 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 A063495 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A063495 From _Harvey P. Dale_, Dec 18 2011: (Start)
%F A063495 a(1)=1, a(2)=18, a(3)=80, a(4)=217, a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) - a(n-4).
%F A063495 G.f.: (x^3+14*x^2+14*x+1)/(1-x)^4. (End)
%F A063495 E.g.f.: (-2 + 4*x + 15*x^2 + 10*x^3)*exp(x)/2 + 1. - _G. C. Greubel_, Dec 01 2017
%t A063495 Table[(2n-1)(5n^2-5n+2)/2,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,18,80,217},40] (* _Harvey P. Dale_, Dec 18 2011 *)
%o A063495 (PARI) a(n) = (2*n - 1)*(5*n^2 - 5*n + 2)/2 \\ _Harry J. Smith_, Aug 23 2009
%o A063495 (PARI) my(x='x+O('x^30)); Vec(serlaplace((-2+4*x+15*x^2+10*x^3)*exp(x)/2 + 1)) \\ _G. C. Greubel_, Dec 01 2017
%o A063495 (Magma) [(2*n-1)*(5*n^2-5*n+2)/2: n in [1..30]]; // _G. C. Greubel_, Dec 01 2017
%Y A063495 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.
%K A063495 nonn,easy
%O A063495 1,2
%A A063495 _N. J. A. Sloane_, Aug 01 2001