A harmonic sequence is defined as a sequence whose reciprocals form an arithmetic sequence. For example: ({10, 12, 15, 20} is harmonic since {1/10, 1/12, 1/15, 1/20} is arithmetic. (Reference:http://perplexus.info/show.php?pid=1557)

Determine three positive integers X,Y and Z satisfying X < Y < Z which belong to a Harmonic sequence with each of X, Y and Z being expressible as the sum of squares of two distinct positive integers such that X + Y = Z + 1 , with Z being less than 2006.