A390708 a(n) = Sum_{k=0..floor(n/3)} binomial(4*n-3*k-3,n-3*k).

1, 1, 10, 85, 725, 6279, 55081, 488034, 4358178, 39163801, 353741245, 3208690588, 29209183319, 266705449726, 2441649187323, 22404042949263, 205987429255437, 1897257391847055, 17502464897959510, 161692063705704301, 1495664578709451181, 13851081315314682804, 128407983202979585460

Offset

0,3

Links

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

Formula

a(n) = [x^n] 1/((1-x^3) * (1-x)^(3*n-2)).

a(n) = Sum_{k=0..n} (-3)^k * binomial(4*n+k,n-k).

Mathematica

Table[Sum[(-3)^k*Binomial[4*n +k, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(4*n-3*k-3, n-3*k));
(Magma) [&+[(-3)^k*Binomial(4*n+k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A371771, A387990, A390704, A390706.

Sequence in context: A144639 A233667 A038235 * A354390 A354318 A346946

Adjacent sequences: A390705 A390706 A390707 * A390709 A390710 A390711

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved