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

0,2

Links

Table of n, a(n) for n=0..20.

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

Prog

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

Crossrefs

Cf. A144904, A371754, A371756.

Sequence in context: A243116 A026033 A005810 * A121203 A368234 A192620

Adjacent sequences: A371752 A371753 A371754 * A371756 A371757 A371758

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved