Find three distinct integers, X, Y and Z, such that X + Y, X + Z, Y + Z, X - Y, X - Z, and Y - Z are all squares of integers.
Apparently, there are many solutions.

Find the set [X, Y, Z] with the smallest X + Y + Z.

Taking the first few X values, 17,68,82,97,153, and placing them into Sloane, does not yield any formula. It's not an arithmetic progression; so I'm wondering what the easy general formula is, even counting the fact that Z=-Y.