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 A375289 #7 Aug 10 2024 11:03:26
%S A375289 1,1,1,0,-5,-14,-26,-29,5,119,348,639,708,-128,-2943,-8571,-15707,
%T A375289 -17340,3347,72718,211126,386091,424633,-87173,-1796760,-5200513,
%U A375289 -9490312,-10398336,2263553,44394265,128099033,233273880,254623403,-58615334,-1096863450,-3155300397
%N A375289 Expansion of (1 - x + x^3)/((1 - x + x^3)^2 + 4*x^4).
%H A375289 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-2,-2,0,-1).
%F A375289 a(n) = 2*a(n-1) - a(n-2) - 2*a(n-3) - 2*a(n-4) - a(n-6).
%F A375289 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-4*k,2*k).
%o A375289 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^3)/((1-x+x^3)^2+4*x^4))
%o A375289 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-4*k, 2*k));
%Y A375289 Cf. A375279.
%K A375289 sign
%O A375289 0,5
%A A375289 _Seiichi Manyama_, Aug 10 2024