---
id: 5900f41a1000cf542c50ff2d
challengeType: 5
title: 'Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements'
---

## Description
<section id='description'>
We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry.
Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. However, using thirty-two tiles it is possible to form two distinct laminae.


If t represents the number of tiles used, we shall say that t = 8 is type L(1) and t = 32 is type L(2).
Let N(n) be the number of t ≤ 1000000 such that t is type L(n); for example, N(15) = 832.
What is ∑ N(n) for 1 ≤ n ≤ 10?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler174()</code> should return 209566.
    testString: assert.strictEqual(euler174(), 209566, '<code>euler174()</code> should return 209566.');

```

</section>

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

<div id='js-seed'>

```js
function euler174() {
  // Good luck!
  return true;
}

euler174();
```

</div>



</section>

## Solution
<section id='solution'>

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