A151849 a(0)=1; a(1)=1; a(2)=0; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=a(j) + a(j + 1) except we add 1 if j=2^i-1.

1, 1, 2, 4, 2, 3, 6, 7, 2, 3, 6, 6, 5, 9, 13, 10, 2, 3, 6, 6, 5, 9, 13, 9, 5, 9, 12, 11, 14, 22, 23, 13, 2, 3, 6, 6, 5, 9, 13, 9, 5, 9, 12, 11, 14, 22, 23, 12, 5, 9, 12, 11, 14, 22, 22, 14, 14, 21, 23, 25, 36, 45, 36, 16, 2, 3, 6, 6, 5, 9, 13, 9, 5, 9, 12, 11, 14, 22, 23, 12, 5, 9, 12, 11, 14