--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:

$$\begin{align} & 1 + 1 + 8 \\ & 1 + 1 + 4 + 4 \\ & 1 + 1 + 2 + 2 + 4 \\ & 2 + 4 + 4 \\ & 2 + 8 \end{align}$$

What is $f({10}^{25})$?

--hints--

numberOfWaysToExpress() should return 178653872807.

assert.strictEqual(numberOfWaysToExpress(), 178653872807);

--seed--

--seed-contents--

function numberOfWaysToExpress() {

  return true;
}

numberOfWaysToExpress();

--solutions--

// solution required