A391127 Expansion of g^2/(1 - x^3*g^3), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 7, 31, 148, 753, 4007, 22026, 124103, 712956, 4160464, 24593297, 146952785, 886176357, 5386253442, 32963243241, 202947767439, 1256168370488, 7812107704743, 48790154813344, 305884946931968, 1924375746078071, 12144857752654912, 76868446264802505

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (3*k+2) * binomial(3*n-6*k+2,n-3*k)/(3*n-6*k+2).

Mathematica

Table[Sum[ (3*k+2)*Binomial[3*n -6*k+2, n-3*k]/(3*n-6*k+2), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k+2)*binomial(3*n-6*k+2, n-3*k)/(3*n-6*k+2));
(Magma) [&+[(3*k+2)*Binomial(3*n-6*k+2, n-3*k)/(3*n-6*k+2): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A391123, A391124, A391130.

Cf. A001764.

Sequence in context: A391123 A391124 A076177 * A335868 A391130 A126033

Adjacent sequences: A391124 A391125 A391126 * A391128 A391129 A391130

Keyword

nonn

Author

Seiichi Manyama, Nov 29 2025

Status

approved