%I #13 Oct 01 2024 07:19:23
%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,2,1,0,1,2,1,0,1,3,3,1,1,3,3,1,1,4,
%T 6,4,2,4,6,4,2,5,10,10,6,6,10,10,6,7,15,20,16,12,16,20,16,13,22,35,36,
%U 28,28,36,36,29,35,57,71,64,56,64,72,65,64,92,128,135
%N a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/2),n-4*k).
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1).
%F G.f.: (1-x^8)/((1-x^4) * (1-x^8-x^9)) = (1+x^4)/(1-x^8-x^9).
%F a(n) = a(n-8) + a(n-9).
%F a(n) = A017867(n) + A017867(n-4).
%o (PARI) a(n) = sum(k=0, n\4, binomial(k\2, n-4*k));
%o (PARI) my(N=80, x='x+O('x^N)); Vec((1+x^4)/(1-x^8-x^9))
%Y Cf. A124789, A134816, A376647.
%Y Cf. A017867.
%K nonn,easy
%O 0,18
%A _Seiichi Manyama_, Oct 01 2024