MathNet 2006 — Part 01 Question 8

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