A392254 a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(k,3*(n-2*k)).

1, 0, 2, 0, 3, 0, 4, 4, 5, 20, 6, 60, 7, 140, 15, 280, 65, 504, 262, 840, 851, 1330, 2322, 2090, 5557, 3520, 12026, 6864, 24052, 15470, 45243, 37310, 81462, 89600, 143434, 206736, 253727, 453356, 464120, 945608, 895377, 1887004, 1821761, 3633940, 3839581, 6827464, 8186573

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-15,0,20,2,-15,-6,6,6,-1,-2,-1).

Formula

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

a(n) = 6*a(n-2) - 15*a(n-4) + 20*a(n-6) + 2*a(n-7) - 15*a(n-8) - 6*a(n-9) + 6*a(n-10) + 6*a(n-11) - a(n-12) - 2*a(n-13) - a(n-14).

Prog

(PARI) a178618(n, k) = sum(j=0, k, (-1)^(k-j)*binomial(n+1, k-j)*binomial(n+3*j, 3*j));
my(A=1, B=1, C=A^3*B, N=2, M=50, x='x+O('x^M), X=1-A*x^2, Y=7); Vec(sum(k=0, (2*N)\3, C^k*a178618(N-1, k)*X^(2*N-3*k)*x^(Y*k))/(X^3-C*x^Y)^N)

Crossrefs

Cf. A392253, A392255.

Cf. A178618, A392044.

Sequence in context: A357475 A390990 A391196 * A066682 A239968 A362369

Adjacent sequences: A392251 A392252 A392253 * A392255 A392256 A392257

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2026

Status

approved