A390619 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(2*k,2*(n-3*k)).

1, 0, 0, 2, 6, 0, 4, 72, 36, 8, 360, 1080, 232, 1344, 10080, 12128, 5616, 60480, 181504, 129312, 292896, 1596800, 2601024, 2179584, 10425280, 31227264, 35328384, 63843200, 267387264, 512262144, 596285440, 1882500096, 5490526464, 8000614400, 13876291584, 46621997568

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,4,12,0,-4,24,-36).

Formula

G.f.: (1-2*x^3-6*x^4) / ((1-2*x^3-6*x^4)^2 - 48*x^7).

a(n) = 4*a(n-3) + 12*a(n-4) - 4*a(n-6) + 24*a(n-7) - 36*a(n-8).

Mathematica

LinearRecurrence[{0, 0, 4, 12, 0, -4, 24, -36}, {1, 0, 0, 2, 6, 0, 4, 72}, 40] (* Harvey P. Dale, May 23 2026 *)

Prog

(PARI) my(A=2, B=3, C=4*A^2*B, N=1, M=40, x='x+O('x^M), X=1-A*x^3-A*B*x^4, Y=7); Vec(sum(k=0, N\2, C^k*binomial(N, 2*k)*X^(N-2*k)*x^(Y*k))/(X^2-C*x^Y)^N)

Crossrefs

Cf. A390781, A391723.

Cf. A376730.

Sequence in context: A108431 A387766 A387479 * A190144 A019967 A377764

Adjacent sequences: A390616 A390617 A390618 * A390620 A390621 A390622

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2025

Status

approved