A390471 a(n) = Sum_{k=0..n} binomial(n+3*k+2,k).

1, 7, 53, 428, 3591, 30859, 269507, 2381233, 21224067, 190464262, 1718577123, 15576393434, 141705054948, 1293231912849, 11834368060398, 108551318841931, 997744761134880, 9187416419219785, 84736319549112253, 782662340868457193, 7238445631648113784

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Formula

G.f.: g^2/((1-4*x*g^3) * (1-x*g)) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[Binomial[n+3*k+2, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)

Prog

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

Crossrefs

Cf. A224274, A387009, A389471, A390335, A390472, A390473, A390474.

Cf. A002293, A390412.

Sequence in context: A163306 A081338 A394233 * A367937 A142981 A350252

Adjacent sequences: A390468 A390469 A390470 * A390472 A390473 A390474

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2025

Status

approved