HMMT November 2017 T2

How many sequences of integers $\left(a_{1}, \ldots, a_{7}\right)$ are there for which $-1 \leq a_{i} \leq 1$ for every $i$, and

$$a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}+a_{4} a_{5}+a_{5} a_{6}+a_{6} a_{7}=4 ?$$