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 A375288 #8 Aug 10 2024 11:03:30
%S A375288 1,2,3,2,-5,-22,-50,-74,-47,122,544,1230,1816,1144,-3029,-13416,
%T A375288 -30267,-44578,-27815,75170,330874,744780,1094243,676196,-1865344,
%U A375288 -8160100,-18326608,-26859600,-16435947,46284926,201243559,450953386,659291863,399432970,-1148383866
%N A375288 Expansion of 1/((1 - x + x^3)^2 + 4*x^4).
%H A375288 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-2,-2,0,-1).
%F A375288 a(n) = 2*a(n-1) - a(n-2) - 2*a(n-3) - 2*a(n-4) - a(n-6).
%F A375288 a(n) = (1/2) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-4*k+2,2*k+1).
%o A375288 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x+x^3)^2+4*x^4))
%o A375288 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-4*k+2, 2*k+1))/2;
%Y A375288 Cf. A375255, A375290.
%Y A375288 Cf. A375278, A375292.
%K A375288 sign
%O A375288 0,2
%A A375288 _Seiichi Manyama_, Aug 10 2024