# Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2
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)?