Advanced Number Theory · Superchallenge problem

A sequence of integers $a_1,a_2,a_3,...$ is defined by $a_0=1,a_1=23$ and $a_{n+2}=46a_{n+1}-520a_{n}$, find the value of $\sum_{i=0}^{\infty}\frac{a_{i}}{39^{i}}.$