Singleton difference

The positive integers, #x, y$, and $z$, are consecutive terms of an arithmetic progression. Given that $n$ is a positive integer, the equation, $x^2 − y^2 − z^2 = n$, has exactly one solution when $n = 20$:

$13^2 − 10^2 − 7^2 = 20$

In fact there are twenty-five values of $n$ below one hundred for which the equation has a unique solution.

How many values of $n$ less than fifty million have exactly one solution?