Get two consecutive whole numbers that add up to a square number e.g 4 and 5 4+5=9 and √9=3 3,4 and 5 is a pythagorable set. 12 and 13 12+13=25 √25=5 5,12 and 13 is a pythagorable set.
The inverse of this is get any odd number (x) and square it. Half the square number and add/take away half to make y and z. x,y and z will be Pythagorean triples.
Once you have these numbers you can times the triples by x to make more Pythagorean triples.
Based on that, the first number in every Pythagorean triple in its simplest form occurs every two numbers (Every odd number).
In its simplest form, any odd integer + the odd integer at the lowest in the previous simplest Pythagorean triple + the next number in the previous Pythagorean triple (not the hypotenuse) = the next number (not the hypotenuse) in the Pythagorean triple of X or the same thing except that with the hypotenuse not =the adjacent. This means that 2x-2+1/2(x-2squared)+/-0.5=1/2xsquared+/-1.