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 A271532 #24 Feb 16 2025 08:33:33
%S A271532 1,-32,123,-304,605,-1056,1687,-2528,3609,-4960,6611,-8592,10933,
%T A271532 -13664,16815,-20416,24497,-29088,34219,-39920,46221,-53152,60743,
%U A271532 -69024,78025,-87776,98307,-109648,121829,-134880,148831,-163712,179553,-196384,214235,-233136,253117,-274208,296439
%N A271532 a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1).
%C A271532 Alternating sum of centered dodecahedral numbers (A005904).
%C A271532 Without signs and up to offset, this is row 5 of the array A284873. - _Andrey Zabolotskiy_, Oct 10 2017
%H A271532 OEIS Wiki, <a href="https://oeis.org/wiki/Centered_Platonic_numbers">Centered Platonic numbers</a>
%H A271532 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%H A271532 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-6,-4,-1)
%F A271532 G.f.: (1 - 28*x + x^2)/(1 + x)^4.
%F A271532 E.g.f.: exp(-x)*(1 - 31*x + 30*x^2 - 5*x^3).
%F A271532 a(n) = -4*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4).
%t A271532 Table[(-1)^n (n + 1) (5 n^2 + 10 n + 1), {n, 0, 38}]
%t A271532 LinearRecurrence[{-4, -6, -4, -1}, {1, -32, 123, -304}, 39]
%o A271532 (Python) for n in range(0,10**3):print((-1)**n*(n+1)*(5*n**2+10*n+1)) # _Soumil Mandal_, Apr 10 2016
%o A271532 (PARI) a(n)=(-1)^n*(n+1)*(5*n^2+10*n+1) \\ _Charles R Greathouse IV_, Jul 26 2016
%Y A271532 Cf. A000578, A004466, A005904, A006527, A005900, A006566.
%K A271532 sign,easy
%O A271532 0,2
%A A271532 _Ilya Gutkovskiy_, Apr 09 2016