Define predecessors of n, P(n), to consist of numbers whose binary representation is obtained from that of n by replacing 10 with 01 or changing a final 1 to a 0; then a(0)=1, a(n) = Sum a(P(n)), n>0.

A004065

Define predecessors of n, P(n), to consist of numbers whose binary representation is obtained from that of n by replacing 10 with 01 or changing a final 1 to a 0; then a(0)=1, a(n) = Sum a(P(n)), n>0.