A373718 Expansion of 1/(1 - x * (1 + x^2)^3).

1, 1, 1, 4, 7, 13, 28, 53, 105, 211, 413, 819, 1624, 3206, 6349, 12565, 24851, 49183, 97315, 192539, 380989, 753836, 1491567, 2951330, 5839638, 11554621, 22862658, 45237262, 89508951, 177107406, 350434385, 693388850, 1371977475, 2714670141, 5371396171

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (1,0,3,0,3,0,1).

Formula

a(n) = a(n-1) + 3*a(n-3) + 3*a(n-5) + a(n-7).

a(n) = Sum_{k=0..floor(3*n/7)} binomial(3*n-6*k,k).

Prog

(PARI) a(n) = sum(k=0, 3*n\7, binomial(3*n-6*k, k));

Crossrefs

Column k=3 of A373717.

Cf. A373720.

Sequence in context: A304004 A293342 A298346 * A122552 A197546 A074862

Adjacent sequences: A373715 A373716 A373717 * A373719 A373720 A373721

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 15 2024

Status

approved