Voozh

A389653

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

1, 2, 9, 53, 343, 2409, 17802, 136336, 1072423, 8612591, 70324162, 582058522, 4872341229, 41177749046, 350871681958, 3011067471081, 26001219131642, 225761871673857, 1969820385759151, 17262314688320809, 151872247740520694, 1340918715721170568

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

a(n) = Sum_{k=0..floor(n/3)} (k+2) * binomial(4*n-11*k+2,n-3*k)/(4*n-11*k+2).

MATHEMATICA

Table[Sum[ (k+2)*Binomial[4* n-11*k+2, n-3*k]/(4*n-11*k+2), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

PROG

(PARI) a(n) = sum(k=0, n\3, (k+2)*binomial(4*n-11*k+2, n-3*k)/(4*n-11*k+2));

(Magma) [&+[(k+2)*Binomial(4*n-11*k+2, n-3*k)/(4*n-11*k+2): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

CROSSREFS

Cf. A391079, A391081, A391083.

Cf. A002293.

Sequence in context: A371226 A367390 A080146 * A391079 A391081 A391083

Adjacent sequences: A389650 A389651 A389652 * A389654 A389655 A389656

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 27 2025

STATUS

approved

URL: https://oeis.org/A389653

⇱ A389653 - OEIS