A387945 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-3*k,n-3*k).

1, 3, 15, 85, 504, 3069, 19020, 119355, 755973, 4822752, 30943692, 199470651, 1290841501, 8380911780, 54566783235, 356139410853, 2329342005540, 15263658912447, 100185583762554, 658561739358240, 4334784368846814, 28566869011053348, 188466413007415995

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

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

Mathematica

Table[Sum[(-3)^k*Binomial[3*n+k+3, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(3*n-3*k, n-3*k));
(Magma) [&+[(-3)^k*Binomial(3*n+k+3, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 04 2026

Crossrefs

Cf. A008620, A105872, A387990.

Cf. A371770, A385250.

Sequence in context: A093593 A212201 A011900 * A371754 A346374 A118342

Adjacent sequences: A387942 A387943 A387944 * A387946 A387947 A387948

Keyword

nonn

Author

Seiichi Manyama, Nov 13 2025

Status

approved