A391063 Expansion of g/(1 - x^3*g^5), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 3, 13, 61, 306, 1611, 8783, 49165, 280952, 1632306, 9613223, 57260961, 344363782, 2088106237, 12752309967, 78368177095, 484268940212, 3007209949548, 18756303411703, 117448294020218, 738072249640971, 4653317643336593, 29424934498838280, 186573488258599197, 1185963942575337717

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (5*k+1) * binomial(3*n-4*k+1,n-3*k)/(3*n-4*k+1).

Mathematica

Table[Sum[ (5*k+1)*Binomial[3*n -4*k+1, n-3*k]/(3*n-4*k+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Dec 01 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (5*k+1)*binomial(3*n-4*k+1, n-3*k)/(3*n-4*k+1));
(Magma) [&+[(5*k+1)*Binomial(3*n-4*k+1, n-3*k)/(3*n-4*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Dec 01 2025

Crossrefs

Cf. A000305, A390486, A390520.

Cf. A390485, A391059, A391061, A391062, A391064, A391065.

Cf. A001764.

Sequence in context: A026704 A046748 A256333 * A200215 A074548 A367059

Adjacent sequences: A391060 A391061 A391062 * A391064 A391065 A391066

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2025

Status

approved