A373906 a(n) = Sum_{k=0..floor(n/4)} binomial(n+2*k,n-4*k).

1, 1, 1, 1, 2, 8, 29, 85, 212, 476, 1016, 2172, 4825, 11213, 26763, 64095, 151851, 354737, 820328, 1889968, 4361521, 10106859, 23509678, 54793282, 127709888, 297336790, 691382201, 1606284377, 3731020629, 8668253125, 20146856893, 46840732201, 108918637566, 253262275888

Offset

0,5

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-14,6,-1).

Formula

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 14*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: 1/(1 - x - x^4/(1 - x)^5).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n+2*k, n-4*k));

Crossrefs

Cf. A003269, A003522, A005252, A038503, A099131.

Cf. A107025, A373904, A373905.

Sequence in context: A333882 A389535 A365760 * A365758 A389132 A389444

Adjacent sequences: A373903 A373904 A373905 * A373907 A373908 A373909

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 22 2024

Status

approved