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 A376727 #11 Oct 03 2024 09:57:39
%S A376727 1,0,0,3,1,0,5,10,1,7,35,21,10,84,126,47,166,462,343,341,1288,1731,
%T A376727 1170,3081,6453,5685,7553,19572,25280,24004,52789,93844,95932,143435,
%U A376727 299577,386536,448673,873754,1411193,1625003,2536215,4639077,6097214,7959492,14238226
%N A376727 Expansion of (1 + x^3 - x^4)/((1 + x^3 - x^4)^2 - 4*x^3).
%H A376727 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,2,0,-1,2,-1).
%F A376727 a(n) = 2*a(n-3) + 2*a(n-4) - a(n-6) + 2*a(n-7) - a(n-8).
%F A376727 a(n) = Sum_{k=0..floor(n/3)} binomial(2*k+1,2*n-6*k+1).
%o A376727 (PARI) my(N=50, x='x+O('x^N)); Vec((1+x^3-x^4)/((1+x^3-x^4)^2-4*x^3))
%o A376727 (PARI) a(n) = sum(k=0, n\3, binomial(2*k+1, 2*n-6*k+1));
%Y A376727 Cf. A099511, A376726, A376728.
%Y A376727 Cf. A376724, A376730.
%K A376727 nonn
%O A376727 0,4
%A A376727 _Seiichi Manyama_, Oct 03 2024