a(0)=0; for n > 0, a(n) is the sum of the partial sums of binary digits of a(n-1) + 1, starting from the least significant digit, and given weights 1, 2, 2^2, etc.
a(4) is computed as follows: a(3) + 1 = 6 = 110_2; the partial sums of digits and their weights are (0,1), (0+1,2), and (0+1+1,4), so the sum of partial sums is 0*1 + 1*2 + 2*4 = 10.
