Counting numbers of the form $u^2-v^2$

Question

Let $C(x) =|\{(u,v)\in\mathbb N_0^2|3\leq u^2-v^2\leq x, u^2-v^2\in\mathbb {2N+1}\}|$. Are there easy ways to get good upper/lower bounds for $C(x)$?

Edit: I just noticed $C(x)=\sum\frac{d(n)}{2}+\lceil\frac{\frac{\lfloor\sqrt{n}\rfloor}{2}}{2}\rceil -1$ where the first sum runs over the odds between $3$ and $N$. Question can be closed.