Pythagorean triple

Pythagorean triple is a triple of integers that follow the following formula:

$a^{2}+b^{2}=c^{2}$

Some of the simplest triples are:

$3^{2}+4^{2}=5^{2}$ and $5^{2}+12^{2}=13^{2}$

Studying these two triples, the reader may have the insight that

$3^{2}=4+5$ and $5^{2}=12+13$

This leads to a trivial sequence that generates some but not all possible triples is based on the positive integers starting with <maht>a=3</math>::

If $a$ is odd, then $b=a^{2}/2-1/2$ and $c=b+1$

If $a$ is even, then $b=a^{2}/4-1$ and $c=b+2$