"""

Define f(0)=1 and f(n) to be the number of different ways n can be expressed as a sum of integer powers of 2 using each power no more than twice.
For example, f(10)=5 since there are five different ways to express 10:
1 + 1 + 8
1 + 1 + 4 + 41 + 1 + 2 + 2 + 4
2 + 4 + 4
2 + 8
What is f(1025)?

"""