Project Euler 173 - Using up to one million tiles how many different "hollow" square laminae can be formed?

Official link:

laminae image

Thought Process

Not a very difficult problem, but not very fun either so I just brute forced it.

A one ring laminae surrounding an n by n square has 4(n+1) squares I find all of the possible laminae less than 1,000,000, then I find all the different sums of laminae that contain other laminae. I then have a list containing all possible laminae such that they use less than a million squares and I return the length of the list

Interactive Code

Enter a number (yourinput)

Code will output the number of different square laminae that can be formed given yourinput number of tiles