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?