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 A376735 #51 Oct 17 2024 10:40:17
%S A376735 1,2,3,4,7,18,43,88,162,298,583,1188,2402,4722,9123,17648,34463,67632,
%T A376735 132382,257748,500244,970790,1885815,3663816,7110990,13783264,
%U A376735 26692422,51672484,100007876,193487262,374149235,723110880,1396927383,2697694410,5208058825
%N A376735 a(n) = Sum_{k=0..floor(n/4)} (n-3*k+1) * binomial(n-3*k,k)^2.
%F A376735 G.f.: (1-x-x^4)/((1-x-x^4)^2 - 4*x^5)^(3/2).
%F A376735 D-finite with recurrence 4*n*(2*n-3)*a(n) +(-22*n^2+43*n-13)*a(n-1) +2*(10*n^2-26*n+15)*a(n-2) -3*(n-1)*(2*n-5)*a(n-3) +8*(-2*n^2-n+16)*a(n-4) +2*(-2*n^2-23*n-15)*a(n-5) +12*(n-1)^2*a(n-6) +4*n*(2*n+5)*a(n-8) -3*(2*n+1)*(n-1)*a(n-9)=0. - _R. J. Mathar_, Oct 17 2024
%o A376735 (PARI) a(n) = sum(k=0, n\4, (n-3*k+1)*binomial(n-3*k, k)^2);
%Y A376735 Cf. A182884, A375565.
%Y A376735 Cf. A246883.
%K A376735 nonn
%O A376735 0,2
%A A376735 _Seiichi Manyama_, Oct 17 2024