A371755 a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-2*k,n-3*k).
1, 4, 28, 221, 1834, 15657, 136137, 1199014, 10661184, 95493145, 860339723, 7788028028, 70777321331, 645359630071, 5901209474518, 54093485799726, 496910913391428, 4573312196055502, 42160889572810597, 389258294230352460, 3598732127428879981
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(4*n-2*k, n-3*k));
Formula
a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(3*n)).
a(n) ~ 2^(8*n + 9/2) / (47 * sqrt(Pi*n) * 3^(3*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024