A391757 a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(2*(n-3*k),2*k).

1, 3, 9, 27, 87, 351, 1539, 6723, 28467, 117531, 479763, 1955907, 7998075, 32807835, 134797203, 554013027, 2276268075, 9348884811, 38388273219, 157620118995, 647198010171, 2657558176443, 10912933399635, 44813051604675, 184020663786507, 755659784907243

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-9,0,12,36,0,0,-36).

Formula

G.f.: (1-3*x-6*x^4) / ((1-3*x-6*x^4)^2 - 72*x^5).

a(n) = 6*a(n-1) - 9*a(n-2) + 12*a(n-4) + 36*a(n-5) - 36*a(n-8).

Prog

(PARI) my(A=2, B=3, C=4*A*B^2, N=1, M=30, x='x+O('x^M), X=1-B*x-A*B*x^4, Y=5); 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. A391724, A391758.

Sequence in context: A146786 A151029 A179263 * A147242 A148924 A113994

Adjacent sequences: A391754 A391755 A391756 * A391758 A391759 A391760

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2025

Status

approved