A391098 Expansion of g/(1 - x^3*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 4, 23, 143, 984, 7176, 54437, 425151, 3395351, 27599795, 227596829, 1899316786, 16009756517, 136110736835, 1165774569673, 10049448742013, 87124402901142, 759151780205120, 6644688736541306, 58395517117711816, 515078659887240951, 4558380366147254571

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (2*k+1) * binomial(4*n-10*k+1,n-3*k)/(4*n-10*k+1).

Mathematica

Table[Sum[ (2*k+1)*Binomial[4* n-10*k+1, n-3*k]/(4*n-10*k+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (2*k+1)*binomial(4*n-10*k+1, n-3*k)/(4*n-10*k+1));
(Magma) [&+[(2*k+1)*Binomial(4*n-10*k+1, n-3*k)/(4*n-10*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A390298, A391100, A391101.

Cf. A002293, A391079.

Sequence in context: A162561 A277921 A390298 * A020079 A391100 A367043

Adjacent sequences: A391095 A391096 A391097 * A391099 A391100 A391101

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2025

Status

approved