A390543 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*n-k+1,n-k).

1, 3, 16, 91, 541, 3300, 20476, 128603, 815083, 5202523, 33394208, 215340628, 1393938716, 9052470696, 58951457956, 384826276443, 2517368308071, 16498064221161, 108301316192416, 711989404587971, 4686927878151661, 30890364553747856, 203812309462607056

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*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+2,n-k).

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

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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n-k+1, n-k));

Crossrefs

Cf. A005809, A371785, A390541, A390542, A390544, A390545.

Cf. A183160, A199033.

Cf. A001764.

Sequence in context: A009124 A393169 A067679 * A099952 A305852 A221764

Adjacent sequences: A390540 A390541 A390542 * A390544 A390545 A390546

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved