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 A376716 #13 Oct 03 2024 09:57:03
%S A376716 1,1,4,11,27,72,189,493,1292,3383,8855,23184,60697,158905,416020,
%T A376716 1089155,2851443,7465176,19544085,51167077,133957148,350704367,
%U A376716 918155951,2403763488,6293134513,16475640049,43133785636,112925716859,295643364939,774004377960
%N A376716 Expansion of (1 - x + x^2)/((1 - x + x^2)^2 - 4*x^2).
%H A376716 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,2,-1).
%F A376716 a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).
%F A376716 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-2*k+1,2*k).
%o A376716 (PARI) my(N=30, x='x+O('x^N)); Vec((1-x+x^2)/((1-x+x^2)^2-4*x^2))
%o A376716 (PARI) a(n) = sum(k=0, n\2, binomial(2*n-2*k+1, 2*k));
%Y A376716 Cf. A000302, A376717, A376718.
%Y A376716 Cf. A182890.
%K A376716 nonn
%O A376716 0,3
%A A376716 _Seiichi Manyama_, Oct 02 2024