A306859 a(n) = Sum_{k=0..floor(n/8)} binomial(n,8*k).

1, 1, 1, 1, 1, 1, 1, 1, 2, 10, 46, 166, 496, 1288, 3004, 6436, 12872, 24328, 43912, 76552, 130816, 223840, 394384, 735472, 1470944, 3124576, 6874336, 15260896, 33550336, 72274816, 151869376, 311058496, 622116992, 1219254400, 2353246336, 4500697216, 8589869056

Offset

0,9

Links

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8).

Formula

G.f.: (1 - x)^7/((1 - x)^8 - x^8).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) for n > 7.

Mathematica

a[n_] := Sum[Binomial[n, 8*k], {k, 0, Floor[n/8]}]; Array[a, 37, 0] (* Amiram Eldar, May 25 2021 *)

Prog

(PARI) {a(n) = sum(k=0, n\8, binomial(n, 8*k))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8-x^8))

Crossrefs

Column 8 of A306846.

Sequence in context: A137334 A209010 A306752 * A212387 A191813 A360412

Adjacent sequences: A306856 A306857 A306858 * A306860 A306861 A306862

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 14 2019

Status

approved