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 A269237 #47 Feb 16 2025 08:33:30
%S A269237 1,34,189,616,1525,3186,5929,10144,16281,24850,36421,51624,71149,
%T A269237 95746,126225,163456,208369,261954,325261,399400,485541,584914,698809,
%U A269237 828576,975625,1141426,1327509,1535464,1766941,2023650,2307361,2619904,2963169,3339106,3749725,4197096
%N A269237 a(n) = (n + 1)^2*(5*n^2 + 10*n + 2)/2.
%C A269237 Partial sums of centered dodecahedral numbers (A005904).
%H A269237 OEIS Wiki, <a href="https://oeis.org/wiki/Centered_Platonic_numbers">Centered Platonic numbers</a>
%H A269237 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%H A269237 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F A269237 G.f.: (1 + 29*x + 29*x^2 + x^3)/(1 - x)^5.
%F A269237 E.g.f.: exp(x)*(2 + 66*x + 122*x^2 + 50*x^3 + 5*x^4)/2.
%F A269237 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A269237 Sum_{n>=0} 1/a(n) = (5 - Pi^2 - sqrt(15)*Pi*cot(sqrt(3/5)*Pi))/9 = 1.0377796966... . - _Vaclav Kotesovec_, Apr 10 2016
%p A269237 A269237:=n->(n + 1)^2*(5*n^2 + 10*n + 2)/2: seq(A269237(n), n=0..50); # _Wesley Ivan Hurt_, Oct 15 2017
%t A269237 Table[(n + 1)^2 ((5 n^2 + 10 n + 2)/2), {n, 0, 35}]
%t A269237 LinearRecurrence[{5, -10, 10, -5, 1}, {1, 34, 189, 616, 1525}, 36]
%o A269237 (PARI) x='x+O('x^99); Vec((1+29*x+29*x^2+x^3)/(1-x)^5) \\ _Altug Alkan_, Apr 10 2016
%o A269237 (Magma) [(n + 1)^2*(5*n^2 + 10*n + 2)/2 : n in [0..50]]; // _Wesley Ivan Hurt_, Oct 15 2017
%Y A269237 Cf. A005904, A006566, A008354, A014820, A037270, A132366.
%K A269237 nonn,easy
%O A269237 0,2
%A A269237 _Ilya Gutkovskiy_, Apr 09 2016