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)?
探索将数表达为2的幂之和的方式数目
记f(0)=1，f(n)是将n表达为2的幂之和，且不同的幂至多使用两次的方式数目。
例如，f(10)=5，即有五种不同的方式表示10：
1 + 1 + 8
1 + 1 + 4 + 41 + 1 + 2 + 2 + 4
2 + 4 + 4
2 + 8
求f(1025)。