In ordinary binary, a number is written as a sum of powers of two, with no repeated terms. For example, 10 = 2+8, written 1010 in binary, and that is the unique binary representation of 10 (order doesn't matter; i.e. 8 + 2 is not different from 2 + 8). Now let's define jumbo binary: We write numbers as sums of powers of two, but we are allowed to repeat a term twice (or not). Thus we can write 10 = 2+8 as well as 1+1+8 and 2+4+4 and 1+1+2+2+4 and 1+1+4+4. Thus 10 has 5 jumbo binary representations (verify that there are no others). Investigate the general case: how many jumbo binary representations are for n?