Question 143
How many sequences of integers $(a_{1}, \ldots, a_{7})$ are there for which $-1 \leq a_{i} \leq 1$ for every $i$, and
$$
a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}+a_{4} a_{5}+a_{5} a_{6}+a_{6} a_{7}=4 ?
$$
$$
a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}+a_{4} a_{5}+a_{5} a_{6}+a_{6} a_{7}=4 ?
$$