A391065 Expansion of g/(1 - x^3*g^9), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 3, 13, 65, 348, 1939, 11096, 64743, 383449, 2298278, 13910658, 84889397, 521665405, 3225143064, 20044356087, 125155684017, 784694037348, 4938030668623, 31178267939672, 197450911430610, 1253886347655206, 7982655364255420, 50937523135245471, 325725115261624207

Offset

0,3

Links

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

Formula

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

Mathematica

Table[Sum[ (9*k+1)*Binomial[3* n+1, n-3*k]/(3*n+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (9*k+1)*binomial(3*n+1, n-3*k))/(3*n+1);
(Magma) [&+[(9*k+1)*Binomial(3*n+1, n-3*k)/(3*n+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A390485, A391059, A391061, A391062, A391063, A391064.

Cf. A001764.

Sequence in context: A126149 A381144 A060927 * A074537 A284714 A200475

Adjacent sequences: A391062 A391063 A391064 * A391066 A391067 A391068

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2025

Status

approved