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Omni-MATH / How many sequences of integers (a₁,…,a₇) are there for which −1≤a_(i)≤1 for every i, and a₁a₂+a₂a₃+a₃a₄+a₄a₅+a₅a₆+a₆a₇=4?

Problem

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problem

How many sequences of integers (a1,…,a7)(a_{1}, \ldots, a_{7}) are there for which −1≤ai≤1-1 \leq a_{i} \leq 1 for every ii, and a1a2+a2a3+a3a4+a4a5+a5a6+a6a7=4a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}+a_{4} a_{5}+a_{5} a_{6}+a_{6} a_{7}=4?
Plain-text mathematical notation (without MathML)
How many sequences of integers (a₁,…,a₇) are there for which −1≤a_(i)≤1 for every i, and a₁a₂+a₂a₃+a₃a₄+a₄a₅+a₅a₆+a₆a₇=4?
Original LaTeX notation
How many sequences of integers $(a_{1}, \ldots, a_{7})$ are there for which $-1 \leq a_{i} \leq 1$ for every $i$, and $a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}+a_{4} a_{5}+a_{5} a_{6}+a_{6} a_{7}=4$?

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Source and history

task_id
abd1ffab-960e-5691-a4e0-34a330f24260
task_key
test--abd1ffab-960e-5691-a4e0-34a330f24260
task_revision_id
1
config / split
/ test

Official source

initial import