Hint video not valid for all even cases

#1

Accroding to the pythagorean triplet hint video, the possible triplet for even number is:
(N/2)^2-1
N
(N/2)^2+1
Consider N=12: the possible pythagorean triplet is:
(12/2)^2-1=6^2-1 = 36-1 = 35
12
(12/2)^2+1 = 37
This does not form a triplet. However, 12 has a pythagorean triplet- (5,12,13).
What am I missing here?

#2

This does form a triplet 35²+12² = 37²