数列证明题

The sequence $\{a_n\}$ is defined as follows: $a_1=0,2a_{n+1}=3a_n+\sqrt{5a_n^2+4}\text{ for }(n\ge 1)$. Prove that for any $n\in {\mathbb{N}}^{+}$, $a_n$​ is an integer.