We shall define a pythagorean polygon to be a convex polygon with the following properties:

• there are at least three vertices,
• no three vertices are aligned,
• each vertex has integer coordinates,
• each edge has integer length.

For a given integer n, define P(n) as the number of distinct pythagorean polygons for which the perimeter is ≤ n.
Pythagorean polygons should be considered distinct as long as none is a translation of another.

You are given that P(4) = 1, P(30) = 3655 and P(60) = 891045.
Find P(120).