---
id: 5900f41a1000cf542c50ff2d
title: >-
  Problem 174: Counting the number of "hollow" square laminae that can form one,
  two, three, ... distinct arrangements
challengeType: 5
forumTopicId: 301809
dashedName: >-
  problem-174-counting-the-number-of-hollow-square-laminae-that-can-form-one-two-three-----distinct-arrangements
---

# --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?

# --hints--

`euler174()` should return 209566.

```js
assert.strictEqual(euler174(), 209566);
```

# --seed--

## --seed-contents--

```js
function euler174() {

  return true;
}

euler174();
```

# --solutions--

```js
// solution required
```