A391130 Expansion of g^2/(1 - x^3*g^4), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 7, 31, 149, 761, 4059, 22348, 126064, 724850, 4232694, 25033450, 149646521, 902736714, 5488516397, 33597424528, 206896370434, 1280845253354, 7966860190967, 49763742848546, 312028231192569, 1963246199604859, 12391431135734067, 78436287364376008

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (4*k+2) * binomial(3*n-5*k+2,n-3*k)/(3*n-5*k+2).

Mathematica

Table[Sum[ (4*k+2)*Binomial[3*n -5*k+2, n-3*k]/(3*n-5*k+2), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (4*k+2)*binomial(3*n-5*k+2, n-3*k)/(3*n-5*k+2));
(Magma) [&+[(4*k+2)*Binomial(3*n-5*k+2, n-3*k)/(3*n-5*k+2): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A391123, A391124, A391127.

Cf. A001764.

Sequence in context: A076177 A391127 A335868 * A126033 A369622 A391306

Adjacent sequences: A391127 A391128 A391129 * A391131 A391132 A391133

Keyword

nonn

Author

Seiichi Manyama, Nov 29 2025

Status

approved