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 A376787 #16 Aug 11 2025 13:02:33
%S A376787 1,0,1,3,1,10,6,21,36,43,127,139,340,540,881,1832,2653,5427,8829,
%T A376787 15550,28642,46805,87756,147575,262751,465591,797864,1437816,2471553,
%U A376787 4383696,7689305,13402819,23752217,41305842,72916606,127708213,223809012,394045411
%N A376787 Expansion of (1 - x^2 + x^3)/((1 - x^2 + x^3)^2 - 4*x^3).
%H A376787 Harvey P. Dale, <a href="/A376787/b376787.txt">Table of n, a(n) for n = 0..1000</a>
%H A376787 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,2,-1).
%F A376787 a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
%F A376787 a(n) = Sum_{k=0..floor(n/2)} binomial(2*k+1,2*n-4*k).
%t A376787 CoefficientList[Series[(1-x^2+x^3)/((1-x^2+x^3)^2-4x^3),{x,0,40}],x] (* or *) LinearRecurrence[{0,2,2,-1,2,-1},{1,0,1,3,1,10},40] (* _Harvey P. Dale_, Aug 11 2025 *)
%o A376787 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2+x^3)/((1-x^2+x^3)^2-4*x^3))
%o A376787 (PARI) a(n) = sum(k=0, n\2, binomial(2*k+1, 2*n-4*k));
%Y A376787 Cf. A376716, A376788.
%Y A376787 Cf. A376723, A376726, A376729.
%K A376787 nonn
%O A376787 0,4
%A A376787 _Seiichi Manyama_, Oct 04 2024