A387678 Expansion of g/(1 + x^3*g^2), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 3, 11, 52, 261, 1374, 7484, 41860, 239052, 1388145, 8171799, 48658094, 292541013, 1773431121, 10828258536, 66531920611, 411062356077, 2552254837562, 15916725942827, 99656423131078, 626202138247370, 3947659825225371, 24960745515499322, 158256000235276253

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (2*k+1) * binomial(3*n-7*k+1,n-3*k)/(3*n-7*k+1).

Mathematica

Table[Sum[(-1)^k*(2*k+1)*Binomial[3*n-7*k+1, n-3*k]/(3*n-7*k+1), {k, 0, Floor[n/3]}], {n, 0, 30}] (* Vincenzo Librandi, Dec 02 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(2*k+1)*binomial(3*n-7*k+1, n-3*k)/(3*n-7*k+1));
(Magma) [&+[(-1)^k*(2*k+1)*Binomial(3*n-7*k+1, n-3*k)/(3*n-7*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Dec 02 2025

Crossrefs

Cf. A089354, A387677.

Cf. A001764.

Sequence in context: A362468 A292927 A367046 * A179322 A014510 A351067

Adjacent sequences: A387675 A387676 A387677 * A387679 A387680 A387681

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2025

Status

approved