A391081 Expansion of g^2/(1 - x^3*g^3), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 53, 345, 2424, 17911, 137153, 1078698, 8661917, 70719546, 585279531, 4898938265, 41399886798, 352745071155, 3026999238663, 26137694758527, 226938425917245, 1980020659673521, 17351190723004606, 152650109366941644, 1347754219937411579

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(3*k+2)*Binomial[4* n-9*k+2, n-3*k]/(4*n-9*k+2), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k+2)*binomial(4*n-9*k+2, n-3*k)/(4*n-9*k+2));
(Magma) [&+[(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..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A389653, A391079, A391083.

Cf. A002293.

Sequence in context: A080146 A389653 A391079 * A391083 A074602 A394148

Adjacent sequences: A391078 A391079 A391080 * A391082 A391083 A391084

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved