A371742 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-k,n-2*k).

1, 3, 16, 92, 551, 3380, 21065, 132771, 843944, 5399802, 34731776, 224361283, 1454557294, 9458829681, 61670895633, 403003997300, 2638776935215, 17308508054848, 113709379928689, 748069400432262, 4927608724973776, 32495826854732633, 214521754579553129

Offset

0,2

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A108081, A371743, A371744.

Cf. A066380, A371754.

Cf. A183160.

Sequence in context: A099952 A305852 A221764 * A213229 A323968 A074555

Adjacent sequences: A371739 A371740 A371741 * A371743 A371744 A371745

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved