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 A376723 #13 Oct 03 2024 13:22:13
%S A376723 1,0,2,2,3,10,7,28,33,64,132,170,408,578,1119,2002,3194,6310,10021,
%T A376723 18666,32353,55450,101443,170672,308744,534820,935936,1663892,2872669,
%U A376723 5111652,8898082,15641802,27538647,48049562,84813451,148219128,260572901,457451088
%N A376723 Expansion of 1/((1 - x^2 - x^3)^2 - 4*x^5).
%H A376723 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,2,-1).
%F A376723 a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
%F A376723 a(n) = (1/2) * Sum_{k=0..floor(n/2)} binomial(2*k+2,2*n-4*k+1).
%o A376723 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x^2-x^3)^2-4*x^5))
%o A376723 (PARI) a(n) = sum(k=0, n\2, binomial(2*k+2, 2*n-4*k+1))/2;
%Y A376723 Cf. A182890, A376724, A376725.
%Y A376723 Cf. A376726, A376729.
%Y A376723 Cf. A375278.
%K A376723 nonn
%O A376723 0,3
%A A376723 _Seiichi Manyama_, Oct 02 2024