Eccoci.

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 $\le n$.
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 $P(120)$.