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a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-2*k,n-3*k).
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%I #9 Apr 05 2024 13:06:13

%S 1,4,28,221,1834,15657,136137,1199014,10661184,95493145,860339723,

%T 7788028028,70777321331,645359630071,5901209474518,54093485799726,

%U 496910913391428,4573312196055502,42160889572810597,389258294230352460,3598732127428879981

%N a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-2*k,n-3*k).

%F a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(3*n)).

%F a(n) ~ 2^(8*n + 9/2) / (47 * sqrt(Pi*n) * 3^(3*n - 1/2)). - _Vaclav Kotesovec_, Apr 05 2024

%o (PARI) a(n) = sum(k=0, n\3, binomial(4*n-2*k, n-3*k));

%Y Cf. A144904, A371754, A371756.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 05 2024