A390298 Expansion of g/(1 - x^3*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 4, 23, 142, 978, 7137, 54163, 423141, 3380062, 27480224, 226641221, 1891545955, 15945663152, 135575825122, 1161265584549, 10011115240466, 86796094401682, 756321790481689, 6620155558163442, 58181764203020977, 513207862840300696, 4541940432627503029

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(4*n-11*k+1,n-3*k)/(4*n-11*k+1).

Mathematica

Table[Sum[ (k+1)*Binomial[4* n-11*k+1, n-3*k]/(4*n-11*k+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (k+1)*binomial(4*n-11*k+1, n-3*k)/(4*n-11*k+1));
(Magma) [&+[(k+1)*Binomial(4*n-11*k+1, n-3*k)/(4*n-11*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A002293, A389653, A391103.

Sequence in context: A091642 A162561 A277921 * A391098 A020079 A391100

Adjacent sequences: A390295 A390296 A390297 * A390299 A390300 A390301

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2025

Status

approved