---
id: 5900f4ab1000cf542c50ffbe
challengeType: 5
title: 'Problem 319: Bounded Sequences'
---

## Description
<section id='description'>
Let x1, x2,..., xn be a sequence of length n such that:
x1 = 2
for all 1 < i ≤ n : xi-1 < xi
for all i and j with 1 ≤ i, j ≤ n : (xi) j < (xj + 1)i

There are only five such sequences of length 2, namely:
{2,4}, {2,5}, {2,6}, {2,7} and {2,8}.
There are 293 such sequences of length 5; three examples are given below:
{2,5,11,25,55}, {2,6,14,36,88}, {2,8,22,64,181}.


Let t(n) denote the number of such sequences of length n.
You are given that t(10) = 86195 and t(20) = 5227991891.


Find t(1010) and give your answer modulo 109.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler319()</code> should return 268457129.
    testString: assert.strictEqual(euler319(), 268457129, '<code>euler319()</code> should return 268457129.');

```

</section>

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

<div id='js-seed'>

```js
function euler319() {
  // Good luck!
  return true;
}

euler319();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
