A371754 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).

1, 3, 15, 85, 505, 3081, 19125, 120173, 761995, 4865697, 31244029, 201544551, 1305039209, 8477521051, 55221311565, 360559717807, 2359123470971, 15463951609491, 101530816122729, 667587477393509, 4395294402200983, 28972295880583861, 191181607835416543

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) ~ 3^(3*n + 5/2) / (17 * sqrt(Pi*n) * 2^(2*n)). - Vaclav Kotesovec, Apr 05 2024

Prog

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

Crossrefs

Cf. A144904, A371755, A371756.

Cf. A066380, A371742.

Sequence in context: A093593 A212201 A011900 * A346374 A118342 A084209

Adjacent sequences: A371751 A371752 A371753 * A371755 A371756 A371757

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved