A391458 Expansion of g^2/(1 + x^3*g^3), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 51, 335, 2364, 17511, 134303, 1057446, 8498115, 69424964, 574844733, 4813486921, 40690941990, 346798845213, 2976661777689, 25708160461067, 223247734992435, 1948116221860923, 17073908081529946, 150228705609723510, 1326518390219586025

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (3*k+2) * binomial(4*n-9*k+2,n-3*k)/(4*n-9*k+2).

Mathematica

Table[Sum[(-1)^k*(3*k+2)*Binomial[4*n-9*k+2, n-3*k]/(4*n-9*k+2), {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(3*k+2)*binomial(4*n-9*k+2, n-3*k)/(4*n-9*k+2));
(Magma) [&+[(-1)^k*(3*k+2)*Binomial(4*n-9*k+2, n-3*k)/(4*n-9*k+2): k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Dec 20 2025

Crossrefs

Cf. A002293, A391081.

Sequence in context: A396432 A374567 A246464 * A391456 A391454 A355397

Adjacent sequences: A391455 A391456 A391457 * A391459 A391460 A391461

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved