Do not forget the evil and odious numbers, complement of each other. But you won't like their g.f.s: A001969 G.f.: sum[k>=0, t(3+2t+3t^2)/(1-t^2)^2 * prod(l=0,k-1,1-t^(2^l)), t=x^2^k]. A000069 G.f.: 1+sum[k>=0, t(2+2t+5t^2-t^4)/(1-t^2)^2 * prod(l=0,k-1,1-t^(2^l)), t=x^2^k]. Good luck! ralf