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 A376717 #13 Oct 03 2024 09:56:59
%S A376717 1,1,1,4,11,22,42,91,205,443,936,1999,4316,9300,19949,42785,91917,
%T A376717 197548,424331,911218,1957086,4203927,9029949,19395031,41657808,
%U A376717 89477119,192189304,412803240,886657081,1904448737,4090567673,8786130132,18871714923,40534529294
%N A376717 Expansion of (1 - x + x^3)/((1 - x + x^3)^2 - 4*x^3).
%H A376717 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,2,0,-1).
%F A376717 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).
%F A376717 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k+1,2*k).
%o A376717 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^3)/((1-x+x^3)^2-4*x^3))
%o A376717 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-4*k+1, 2*k));
%Y A376717 Cf. A000302, A376716, A376718.
%Y A376717 Cf. A375278, A375279.
%K A376717 nonn
%O A376717 0,4
%A A376717 _Seiichi Manyama_, Oct 02 2024