A390359 a(n) = Sum_{k=0..n} binomial(3*n+3*k,n-k).

1, 4, 25, 166, 1125, 7697, 52933, 365137, 2523563, 17462647, 120937831, 838016430, 5809007778, 40276886567, 279303253405, 1937023574420, 13434233140312, 93174174889226, 646208161889308, 4481628609583854, 31079945382792303, 215526938057837140, 1494503510752987611

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/((1-3*x*g^2) * (1-x*g^6)) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[Binomial[3* n+3*k, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

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

Crossrefs

Cf. A038736, A045721, A066380, A188675, A388043, A390358.

Cf. A001764.

Sequence in context: A184755 A357223 A074422 * A128419 A372216 A226945

Adjacent sequences: A390356 A390357 A390358 * A390360 A390361 A390362

Keyword

nonn

Author

Seiichi Manyama, Nov 02 2025

Status

approved