yaworsw/euler-manager

---
:id: 174
:name: Counting the number of "hollow" square laminae that can form one, two, three,
  ... distinct arrangements
:url: https://projecteuler.net/problem=174
:content: |+
  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.

   ![]({{ images_dir }}/p173_square_laminas.gif)

  If <var>t</var> represents the number of tiles used, we shall say that <var>t</var> = 8 is type L(1) and <var>t</var> = 32 is type L(2).

  Let N(<var>n</var>) be the number of <var>t</var> ≤ 1000000 such that <var>t</var> is type L(<var>n</var>); for example, N(15) = 832.

  What is ∑ N(<var>n</var>) for 1 ≤ <var>n</var> ≤ 10?