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 A375290 #8 Aug 10 2024 11:03:18
%S A375290 1,2,3,4,3,-4,-21,-52,-98,-144,-143,0,440,1368,2891,4752,5831,3438,
%T A375290 -7330,-33384,-81044,-148610,-211283,-197280,39748,732646,2152660,
%U A375290 4423184,7089816,8360270,4071395,-13171888,-53480919,-125422768,-224380607,-309560644,-268524883
%N A375290 Expansion of 1/((1 - x + x^4)^2 + 4*x^5).
%H A375290 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,-2,-2,0,0,-1).
%F A375290 a(n) = 2*a(n-1) - a(n-2) - 2*a(n-4) - 2*a(n-5) - a(n-8).
%F A375290 a(n) = (1/2) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(2*n-6*k+2,2*k+1).
%o A375290 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x+x^4)^2+4*x^5))
%o A375290 (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(2*n-6*k+2, 2*k+1))/2;
%Y A375290 Cf. A375255, A375288.
%Y A375290 Cf. A375293.
%K A375290 sign
%O A375290 0,2
%A A375290 _Seiichi Manyama_, Aug 10 2024