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, $x^2 − y^2 − z^2 = n$, has exactly two solutions is $n = 27$:

$34^2 − 27^2 − 20^2 = 12^2 − 9^2 − 6^2 = 27$

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?