A386496 G.f. A(x) satisfies A(x) = 1 + x*(1+x^3)*A(x)^3.

1, 1, 3, 12, 56, 279, 1464, 7972, 44631, 255279, 1485309, 8763474, 52308615, 315300734, 1916541654, 11734469820, 72304205945, 448014505908, 2789827548873, 17449819111380, 109581892365993, 690644955183813, 4367126156306434, 27697268359518348, 176144689605045348

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * A001764(n-3*k).

Mathematica

Table[Sum[Binomial[n-3*k, k]*Binomial[3*(n-3*k), n-3*k]/(2*(n-3*k)+1), {k, 0, Floor[n/4]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(3*(n-3*k), n-3*k)/(2*(n-3*k)+1));
(Magma) [&+[Binomial(n-3*k, k)*Binomial(3*(n-3*k), n-3*k)/(2*(n-3*k)+1): k in [0..Floor(n/4)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 16 2025

Crossrefs

Cf. A364475, A367059.

Cf. A001764.

Sequence in context: A107318 A379160 A390486 * A389285 A176281 A050147

Adjacent sequences: A386493 A386494 A386495 * A386497 A386498 A386499

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 18 2025

Status

approved