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 A376726 #10 Oct 03 2024 08:31:00
%S A376726 1,0,3,1,5,10,8,35,30,85,137,201,476,616,1357,2172,3735,7193,11213,
%T A376726 21782,36064,64095,115130,193769,354737,604049,1074008,1889968,
%U A376726 3273785,5839608,10106859,17880785,31325077,54793282,96710296,168730043,297336790,520856765,913684857
%N A376726 Expansion of (1 + x^2 - x^3)/((1 + x^2 - x^3)^2 - 4*x^2).
%H A376726 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,2,-1).
%F A376726 a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
%F A376726 a(n) = Sum_{k=0..floor(n/2)} binomial(2*k+1,2*n-4*k+1).
%o A376726 (PARI) my(N=40, x='x+O('x^N)); Vec((1+x^2-x^3)/((1+x^2-x^3)^2-4*x^2))
%o A376726 (PARI) a(n) = sum(k=0, n\2, binomial(2*k+1, 2*n-4*k+1));
%Y A376726 Cf. A099511, A376727, A376728.
%Y A376726 Cf. A376723, A376729.
%K A376726 nonn
%O A376726 0,3
%A A376726 _Seiichi Manyama_, Oct 03 2024