---
id: 5900f4151000cf542c50ff28
challengeType: 5
title: 'Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2'
---
## Description
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)?
## Instructions
## Tests
```yml
tests:
- text: euler169() should return 178653872807.
testString: assert.strictEqual(euler169(), 178653872807, 'euler169() should return 178653872807.');
```
## Challenge Seed
```js
function euler169() {
// Good luck!
return true;
}
euler169();
```