A151853 a(0)=0; a(1)=1; a(2)=0; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=a(j) + 2*a(j + 1) except we add 1 if j=2^i-1.

0, 1, 2, 6, 2, 5, 14, 11, 2, 5, 14, 10, 12, 33, 36, 16, 2, 5, 14, 10, 12, 33, 36, 15, 12, 33, 34, 34, 78, 105, 68, 21, 2, 5, 14, 10, 12, 33, 36, 15, 12, 33, 34, 34, 78, 105, 68, 20, 12, 33, 34, 34, 78, 105, 66, 39, 78, 101, 102, 190, 288, 241, 110, 26, 2, 5, 14, 10, 12, 33, 36, 15, 12