A151857 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) + 2*a(j + 1) except we add 1 if j=2^i-1.

1, 1, 3, 8, 3, 7, 19, 15, 3, 7, 19, 14, 17, 45, 49, 22, 3, 7, 19, 14, 17, 45, 49, 21, 17, 45, 47, 48, 107, 143, 93, 29, 3, 7, 19, 14, 17, 45, 49, 21, 17, 45, 47, 48, 107, 143, 93, 28, 17, 45, 47, 48, 107, 143, 91, 55, 107, 139, 143, 262, 393, 329, 151, 36, 3, 7, 19, 14, 17, 45, 49