A371817 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(4*n-3*k-1,n-3*k).

1, 3, 21, 164, 1353, 11508, 99808, 877425, 7790745, 69704921, 627438606, 5675535000, 51546958296, 469764721533, 4293594852225, 39341599326304, 361271345551257, 3323924166943410, 30634431485945569, 282767849049333909, 2613630939017216898

Offset

0,2

Links

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

Formula

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

a(n) = binomial(4*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-4*n)/3, (2-4*n)/3, 1-4*n/3], -1). - Stefano Spezia, Apr 07 2024

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(4*n-3*k-1, n-3*k));

Crossrefs

Cf. A120305, A262977, A371816.

Cf. A371771.

Sequence in context: A179815 A118353 A365132 * A262977 A361375 A371771

Adjacent sequences: A371814 A371815 A371816 * A371818 A371819 A371820

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2024

Status

approved