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A306859
a(n) = Sum_{k=0..floor(n/8)} binomial(n,8*k).
3
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
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 * A373913 A212387 A191813
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 14 2019
STATUS
approved