---
id: 5900f4eb1000cf542c50fffd
title: 'Problem 382: Generating polygons'
challengeType: 5
forumTopicId: 302046
dashedName: problem-382-generating-polygons
---

# --description--

A polygon is a flat shape consisting of straight line segments that are joined to form a closed chain or circuit. A polygon consists of at least three sides and does not self-intersect.

A set S of positive numbers is said to generate a polygon P if: no two sides of P are the same length, the length of every side of P is in S, and S contains no other value.

For example: The set {3, 4, 5} generates a polygon with sides 3, 4, and 5 (a triangle). The set {6, 9, 11, 24} generates a polygon with sides 6, 9, 11, and 24 (a quadrilateral). The sets {1, 2, 3} and {2, 3, 4, 9} do not generate any polygon at all.

Consider the sequence s, defined as follows:s1 = 1, s2 = 2, s3 = 3 sn = sn-1 + sn-3 for n > 3.

Let Un be the set {s1, s2, ..., sn}. For example, U10 = {1, 2, 3, 4, 6, 9, 13, 19, 28, 41}. Let f(n) be the number of subsets of Un which generate at least one polygon. For example, f(5) = 7, f(10) = 501 and f(25) = 18635853.

Find the last 9 digits of f(1018).

# --hints--

`euler382()` should return 697003956.

```js
assert.strictEqual(euler382(), 697003956);
```

# --seed--

## --seed-contents--

```js
function euler382() {

  return true;
}

euler382();
```

# --solutions--

```js
// solution required
```