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a(n)=a(n-1)+a(n-2)-d, where d=a(n/2) if n is even, else d=0; 2 initial terms.
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%I #8 Jun 06 2020 08:44:30

%S 1,0,1,1,2,2,4,5,9,12,21,31,52,79,131,205,336,532,868,1388,2256,3623,

%T 5879,9471,15350,24769,40119,64809,104928,169606,274534,443935,718469,

%U 1162068,1880537,3042073,4922610,7963815,12886425

%N a(n)=a(n-1)+a(n-2)-d, where d=a(n/2) if n is even, else d=0; 2 initial terms.

%H Robert Israel, <a href="/A050192/b050192.txt">Table of n, a(n) for n = 1..4780</a>

%F G.f. g(z) satisfies (1-z-z^2)*g(z) - g(z^2) = z. - _Robert Israel_, Jun 05 2020

%p G:= z -> z:

%p for i from 1 to 7 do

%p G:= unapply(convert(series((z-G(z^2))/(1-z-z^2),z,2^i+1),polynom),z)

%p od:

%p seq(coeff(G(z),z,i),i=1..2^7); # _Robert Israel_, Jun 05 2020

%K nonn

%O 1,5

%A _Clark Kimberling_