A371758 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-1,n-3*k).

1, 1, 3, 11, 39, 141, 519, 1933, 7263, 27479, 104543, 399543, 1532779, 5899167, 22766607, 88073091, 341425551, 1326019653, 5158412943, 20096457549, 78396460299, 306190920837, 1197181197567, 4685523856881, 18354865147011, 71962695111841, 282357198103815

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

a(n) = binomial(2*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-2*n)/3, 2*(1-n)/3, 1-2*n/3], 1). - Stefano Spezia, Apr 06 2024

From Vaclav Kotesovec, Apr 08 2024: (Start)

Recurrence: 3*n*(7*n-11)*a(n) = 6*(2*n-3)*(7*n-4)*a(n-1) - n*(7*n-11)*a(n-2) + 2*(2*n-3)*(7*n-4)*a(n-3).

a(n) ~ 2^(2*n+2) / (7*sqrt(Pi*n)). (End)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k-1, n-3*k));

Crossrefs

Cf. A371770, A371771, A371772.

Cf. A144904, A371773, A371777.

Sequence in context: A007482 A134760 A257290 * A281482 A132889 A245390

Adjacent sequences: A371755 A371756 A371757 * A371759 A371760 A371761

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved