A390588 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n-k+3,n-k).

1, 5, 29, 174, 1068, 6656, 41941, 266492, 1704377, 10957957, 70757132, 458544280, 2980752184, 19427502404, 126912484101, 830740684920, 5447524136259, 35778391154159, 235320088249429, 1549718825607734, 10217632324187824, 67438185088013984, 445533468374765164

Offset

0,2

Links

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

Formula

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

a(n) = Sum_{k=0..n} (-2)^k * binomial(3*n+4,n-k).

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(3*n+4,k) * binomial(3*n-k+3,n-k).

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

Mathematica

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

Crossrefs

Cf. A183160, A199033, A390543, A390591.

Cf. A172025, A390589, A390590.

Cf. A004319, A075045.

Cf. A001764, A385250.

Sequence in context: A083066 A327557 A384368 * A163611 A160906 A163073

Adjacent sequences: A390585 A390586 A390587 * A390589 A390590 A390591

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2025

Status

approved