HMMT 2006 A4

Let $a_{1}, a_{2}, \ldots$ be a sequence defined by $a_{1}=a_{2}=1$ and $a_{n+2}=a_{n+1}+a_{n}$ for $n \geq 1$. Find

$$\sum_{n=1}^{\infty} \frac{a_{n}}{4^{n+1}}$$