A390775 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k,2*(n-3*k)).

1, 0, 0, 2, 0, 0, 4, 12, 0, 8, 72, 0, 16, 288, 144, 32, 960, 1440, 64, 2880, 8640, 1856, 8064, 40320, 24448, 21504, 161280, 194048, 76032, 580608, 1162240, 511488, 1935360, 5808128, 4070400, 6331392, 25550848, 28182528, 23721984, 102195200, 166146048

Offset

0,4

Links

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

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

Formula

G.f.: (1-2*x^3) / ((1-2*x^3)^2 - 12*x^7).

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

Mathematica

CoefficientList[Series[(1-2*x^3)/((1-2*x^3)^2-12*x^7), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 29 2025 *)

Prog

(PARI) my(A=2, B=3, C=A^2*B, N=1, M=50, x='x+O('x^M), X=1-A*x^3, 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)
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-2*x^3)/((1-2*x^3)^2-12*x^7)); // Vincenzo Librandi, Dec 29 2025

Crossrefs

Cf. A391960, A391961.

Cf. A390619.

Sequence in context: A231037 A048243 A159814 * A169774 A302689 A289088

Adjacent sequences: A390772 A390773 A390774 * A390776 A390777 A390778

Keyword

nonn

Author

Seiichi Manyama, Dec 23 2025

Status

approved