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 A376786 #11 Oct 04 2024 05:43:36
%S A376786 1,3,5,7,10,21,48,99,183,326,602,1165,2282,4396,8318,15675,29743,
%T A376786 56841,108765,207510,394809,750880,1429845,2725685,5196420,9901692,
%U A376786 18859649,35921156,68432064,130388316,248437405,473322419,901717453,1717851555,3272777450
%N A376786 Expansion of (1 + x - x^4)/((1 + x - x^4)^2 - 4*x).
%H A376786 <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 A376786 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) + 2*a(n-5) - a(n-8).
%F A376786 a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-6*k+1,2*k+1).
%o A376786 (PARI) my(N=40, x='x+O('x^N)); Vec((1+x-x^4)/((1+x-x^4)^2-4*x))
%o A376786 (PARI) a(n) = sum(k=0, n\4, binomial(2*n-6*k+1, 2*k+1));
%Y A376786 Cf. A099511, A376785.
%Y A376786 Cf. A375282, A375283, A376718.
%K A376786 nonn
%O A376786 0,2
%A A376786 _Seiichi Manyama_, Oct 04 2024