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?