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 A376729 #12 Oct 03 2024 08:30:55
%S A376729 1,0,1,1,1,6,2,15,16,29,71,73,212,276,541,1016,1497,3189,4825,9162,
%T A376729 16022,26763,50424,82869,151851,262705,456520,820328,1401913,2511824,
%U A376729 4361521,7657481,13528913,23509678,41633002,72630919,127709888,224418509,392539055,691382201
%N A376729 Expansion of (1 - x^2 - x^3)/((1 - x^2 - x^3)^2 - 4*x^5).
%H A376729 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,2,-1).
%F A376729 a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
%F A376729 a(n) = Sum_{k=0..floor(n/2)} binomial(2*k,2*n-4*k).
%o A376729 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2-x^3)/((1-x^2-x^3)^2-4*x^5))
%o A376729 (PARI) a(n) = sum(k=0, n\2, binomial(2*k, 2*n-4*k));
%Y A376729 Cf. A108479, A376730, A376731.
%Y A376729 Cf. A376723, A376726.
%K A376729 nonn
%O A376729 0,6
%A A376729 _Seiichi Manyama_, Oct 03 2024