A389239 a(n) = Sum_{k=0..n} binomial(n+3*k,k).

1, 5, 34, 263, 2159, 18312, 158536, 1391999, 12348587, 110408669, 993288215, 8980902802, 81537707501, 742853687870, 6787829985218, 62181965801769, 570901292982498, 5251748837209879, 48394554894379276, 446640050862838569, 4127802345866735173

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/((1-4*x*g^3) * (1-x*g)) where g = 1+x*g^4 is the g.f. of A002293.

a(n) ~ 2^(8*n + 13/2) / (55 * sqrt(Pi*n) * 3^(3*n + 1/2)). - Vaclav Kotesovec, Nov 04 2025

Mathematica

Table[Sum[Binomial[n+3*k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+3*k, k));
(Magma) [&+[Binomial(n + 3*k, k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A000079, A001700, A388043, A390384, A390385, A390386, A390387.

Cf. A002293, A130458, A390383.

Sequence in context: A002776 A333804 A081342 * A248055 A365218 A387475

Adjacent sequences: A389236 A389237 A389238 * A389240 A389241 A389242

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2025

Status

approved