Squares dissection

Consider the square with side = 720.

We can dissect it in 3 Pythagorean triangles:
- (720, 210, 750)
- (510, 272, 578)
- (448, 720, 848)


We represent this dissection as : c1,c2,c3 = 720,210,272 ($c_2\le \frac{c_1}{2}$)

How many squares with integer sides $\le 20000$ can be dissected this way?

Anser format: $Count,\sum c_1,\sum c_2,\sum c_3$


You are given: 3,2040,1035,569 for a threshold of 1000

[My timing: 24 sec]