--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 $\sum N(n)$ for $1 ≤ n ≤ 10$?

--hints--

hollowSquareLaminaeDistinctArrangements() should return 209566.

assert.strictEqual(hollowSquareLaminaeDistinctArrangements(), 209566);

--seed--

--seed-contents--

function hollowSquareLaminaeDistinctArrangements() {

  return true;
}

hollowSquareLaminaeDistinctArrangements();

--solutions--

// solution required