Same differences

Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer, n, for which the equation, x² − y² − z² = n, has exactly two solutions is n = 27:

34² − 27² − 20² = 12² − 9² − 6² = 27

It turns out that n = 1155 is the least value which has exactly ten solutions.

How many values of n less than one million have exactly ten distinct solutions?

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