A371776 a(n) = Sum_{k=0..floor(n/3)} binomial(5*n-k+1,n-3*k).

1, 6, 55, 561, 6005, 66080, 740342, 8400074, 96206994, 1109874635, 12877808194, 150122945518, 1756887201266, 20628519611407, 242891806678851, 2866906127955287, 33910670558191711, 401857349039547372, 4770115555036932777, 56706219260783415643

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = [x^n] 1/(((1-x)^2-x^3) * (1-x)^(4*n)).

Mathematica

Table[Sum[Binomial[5n-k+1, n-3k], {k, 0, Floor[n/3]}], {n, 0, 20}] (* Harvey P. Dale, May 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(5*n-k+1, n-3*k));

Crossrefs

Cf. A371773, A371774, A371775.

Sequence in context: A121661 A118836 A079589 * A372210 A365840 A006200

Adjacent sequences: A371773 A371774 A371775 * A371777 A371778 A371779

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved