A390486 a(n) = Sum_{k=0..floor(n/4)} (5*k+1) * binomial(3*n-7*k+1,n-4*k)/(3*n-7*k+1).

1, 1, 3, 12, 56, 279, 1461, 7934, 44284, 252500, 1464452, 8612607, 51241929, 307870618, 1865311344, 11383768925, 69915894616, 431811981838, 2680222536507, 16709982342541, 104596250143468, 657090360644485, 4141518159456841, 26181526281172322, 165967226609291162

Offset

0,3

Links

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

Formula

G.f.: g/(1-x^4*g^5) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(5*k+1)*Binomial[3*n-7*k+1, n-4*k]/(3*n-7*k+1), {k, 0, Floor[n/4]}], {n, 0, 30}] (* Vincenzo Librandi, Nov 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, (5*k+1)*binomial(3*n-7*k+1, n-4*k)/(3*n-7*k+1));
(Magma) [&+[(5*k+1)*Binomial(3*n-7*k+1, n-4*k)/(3*n-7*k+1): k in [0..Floor(n/4)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A109957, A390485.

Cf. A001764.

Sequence in context: A284843 A107318 A379160 * A386496 A389285 A176281

Adjacent sequences: A390483 A390484 A390485 * A390487 A390488 A390489

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved