A004065 Define predecessors of n, P(n), to consist of numbers whose binary representation is obtained from that of n by replacing 10 by 01 or changing a final 1 to a 0; then a(0)=1, a(n) = Sum f(P(n)), n>0.

1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 5, 7, 5, 12, 12, 12, 1, 4, 9, 16, 14, 42, 54, 66, 14, 56, 110, 176, 110, 286, 286, 286, 1, 5, 14, 30, 28, 100, 154, 220, 42, 198, 462, 858, 572, 1716, 2002, 2288, 42, 240, 702, 1560, 1274, 4550, 6552, 8840, 1274, 5824, 12376