A390518 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (5*k+1) * binomial(3*n-7*k+1,n-4*k)/(3*n-7*k+1).

1, 1, 3, 12, 54, 267, 1395, 7570, 42244, 240872, 1397154, 8217927, 48900757, 293846186, 1780582056, 10868056429, 66756409248, 412343484034, 2559641114905, 15959696913309, 99908427806528, 627690680859013, 3956509410585793, 25013666433229546, 158574159456493752

Offset

0,3

Links

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

Formula

G.f.: g/(1+x^4*g^5) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(-1)^k*(5*k+1)*Binomial[3*n-7*k+1, n-4*k]/(3*n-7*k+1), {k, 0, Floor[n/4]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\4, (-1)^k*(5*k+1)*binomial(3*n-7*k+1, n-4*k)/(3*n-7*k+1));
(Magma) [&+[(-1)^k* (5*k+1)*Binomial(3*n-7*k+1, n-4*k)/(3*n-7*k+1): k in [0..Floor(n/4)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 13 2025

Crossrefs

Cf. A089354, A389697, A390517.

Cf. A001764, A390486.

Sequence in context: A270489 A388857 A390171 * A335819 A263853 A266083

Adjacent sequences: A390515 A390516 A390517 * A390519 A390520 A390521

Keyword

nonn

Author

Seiichi Manyama, Nov 08 2025

Status

approved