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 A371758 #31 Apr 08 2024 18:48:13
%S A371758 1,1,3,11,39,141,519,1933,7263,27479,104543,399543,1532779,5899167,
%T A371758 22766607,88073091,341425551,1326019653,5158412943,20096457549,
%U A371758 78396460299,306190920837,1197181197567,4685523856881,18354865147011,71962695111841,282357198103815
%N A371758 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-1,n-3*k).
%F A371758 a(n) = [x^n] 1/((1-x^3) * (1-x)^n).
%F A371758 a(n) = binomial(2*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-2*n)/3, 2*(1-n)/3, 1-2*n/3], 1). - _Stefano Spezia_, Apr 06 2024
%F A371758 From _Vaclav Kotesovec_, Apr 08 2024: (Start)
%F A371758 Recurrence: 3*n*(7*n-11)*a(n) = 6*(2*n-3)*(7*n-4)*a(n-1) - n*(7*n-11)*a(n-2) + 2*(2*n-3)*(7*n-4)*a(n-3).
%F A371758 a(n) ~ 2^(2*n+2) / (7*sqrt(Pi*n)). (End)
%o A371758 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k-1, n-3*k));
%Y A371758 Cf. A371770, A371771, A371772.
%Y A371758 Cf. A144904, A371773, A371777.
%K A371758 nonn
%O A371758 0,3
%A A371758 _Seiichi Manyama_, Apr 05 2024