A390541 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(3*k+1,k).

1, 3, 18, 102, 613, 3755, 23377, 147167, 934408, 5972492, 38379673, 247718087, 1604764909, 10428457971, 67950502389, 443788258155, 2904320734836, 19041267622584, 125038439723991, 822271053113409, 5414375650645986, 35693621227289694, 235556873323331346

Offset

0,2

Links

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

Formula

G.f.: g/((1-3*x*g^2) * (1+x)) where g = 1+x*g^3 is the g.f. of A001764.

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[3* k+1, k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(3*k+1, k));
(Magma) [&+[(-1)^(n-k)*Binomial(3*k+1, k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Jan 04 2026

Crossrefs

Cf. A005809, A371785, A390542, A390543, A390544, A390545.

Cf. A001764, A045721, A263134.

Sequence in context: A038158 A327828 A009021 * A303519 A124408 A136779

Adjacent sequences: A390538 A390539 A390540 * A390542 A390543 A390544

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved