Let $a_{n}$ be the number of pairs of integers $(x, y) \in \mathbb{Z}^{2}$ such that $x^{2}+y^{2} \leqslant n^{2}$. What is the radius of convergence of the series $\sum_{n=0}^{\infty} a_{n} z^{n}$ ? [You may use the comparison test, provided you state it clearly.]