A391758 a(n) = Sum_{k=0..floor(n/4)} (n-3*k+1) * 2^k * 3^(n-3*k) * binomial(2*(n-3*k),2*k).

1, 6, 27, 108, 417, 1782, 8343, 40176, 190377, 876906, 3947211, 17522244, 77243517, 339290046, 1486173663, 6490123704, 28248529761, 122547210930, 530018594883, 2286202048812, 9838251072261, 42248728829286, 181086392267559, 774818305073568, 3309874281409257

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-57,-72,-216,648,-216,-432,-1944,0,864,2592,0,0,-1296).

Formula

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

a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 57*a(n-4) - 72*a(n-5) - 216*a(n-6) + 648*a(n-7) - 216*a(n-8) - 432*a(n-9) - 1944*a(n-10) + 864*a(n-12) + 2592*a(n-13) - 1296*a(n-16).

Prog

(PARI) my(A=2, B=3, C=4*A*B^2, N=2, 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, A391757.

Sequence in context: A220529 A027471 A305780 * A037695 A318638 A094829

Adjacent sequences: A391755 A391756 A391757 * A391759 A391760 A391761

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2025

Status

approved