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?