#Pythagoreans

• a = 2n+1
• b = 2n^2+2n
• c = 2n^2+2n+1
• A=4n+4
• B=4n^2+8n+3
• C=4n^2+8n+5

You can start from n^2 and move forward/backwards by 'a' ((n+/-1)^2) or 'A' ((n+/-2)^2). 

You can plug in any 'abc' (or 'bac') or 'ABC' (or 'BAC') below to get the Universe of Pythagorean Triples.  This works for negative numbers as well as positive. 

T0 = 'abc' (or 'bac') or 'ABC' (or 'BAC')
T3 = next T0.

Example t1 a b c t2 a b c t3 a b c

New A 1 -2 2 2 -1 2 2 -2 3

New B 1 2 2 2 1 2 2 2 3

New C -1 2 2 -2 1 2 -2 2 3

New A Prime 2 1 -1 -2 2 2 -2 1 3

New B Prime 2 1 1 2 -2 2 2 -1 3

New C Prime 2 -1 1 2 2 2 2 1 3

More explanation for the transforms can be found here.