---
id: 5900f4951000cf542c50ffa8
challengeType: 5
title: 'Problem 297: Zeckendorf Representation'
forumTopicId: 301949
---

## Description
<section id='description'>
Each new term in the Fibonacci sequence is generated by adding the previous two terms.
Starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89.
Such a sum is called the Zeckendorf representation of the number.

For any integer n>0, let z(n) be the number of terms in the Zeckendorf representation of n.
Thus, z(5) = 1, z(14) = 2, z(100) = 3 etc.
Also, for 0<n<106, ∑ z(n) = 7894453.

Find ∑ z(n) for 0<n<1017.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler297()</code> should return 2252639041804718000.
    testString: assert.strictEqual(euler297(), 2252639041804718000);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler297() {

  return true;
}

euler297();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>