# Problem 173: Using up to one million tiles how many different "hollow" square laminae can be formed?

![graphic](img173.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. For
example, using exactly thirty-two square tiles we can form two different
square laminae: With one-hundred tiles, and not necessarily using all of
the tiles at one time, it is possible to form forty-one different square
laminae. Using up to one million tiles how many different square laminae
can be formed?