# Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements

![graphic](img174.gif)

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?