%I #19 May 26 2021 00:55:05
%S 1,1,1,1,1,1,1,1,2,10,46,166,496,1288,3004,6436,12872,24328,43912,
%T 76552,130816,223840,394384,735472,1470944,3124576,6874336,15260896,
%U 33550336,72274816,151869376,311058496,622116992,1219254400,2353246336,4500697216,8589869056
%N a(n) = Sum_{k=0..floor(n/8)} binomial(n,8*k).
%H Seiichi Manyama, <a href="/A306859/b306859.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8).
%F G.f.: (1 - x)^7/((1 - x)^8 - x^8).
%F 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.
%t a[n_] := Sum[Binomial[n,8*k], {k,0,Floor[n/8]}]; Array[a, 37, 0] (* _Amiram Eldar_, May 25 2021 *)
%o (PARI) {a(n) = sum(k=0, n\8, binomial(n, 8*k))}
%o (PARI) N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8-x^8))
%Y Column 8 of A306846.
%K nonn,easy
%O 0,9
%A _Seiichi Manyama_, Mar 14 2019