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Omni-MATH / Count the number of sequences a₁,a₂,a₃,a₄,a₅ of integers such that a_(i)≤1 for all i and all partial sums (a₁,a₁+a₂, etc.) are non-negative.

Problem

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problem

Count the number of sequences a1,a2,a3,a4,a5a_{1}, a_{2}, a_{3}, a_{4}, a_{5} of integers such that ai≤1a_{i} \leq 1 for all ii and all partial sums (a1,a1+a2\left(a_{1}, a_{1}+a_{2}\right., etc.) are non-negative.
Plain-text mathematical notation (without MathML)
Count the number of sequences a₁,a₂,a₃,a₄,a₅ of integers such that a_(i)≤1 for all i and all partial sums (a₁,a₁+a₂, etc.) are non-negative.
Original LaTeX notation
Count the number of sequences $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ of integers such that $a_{i} \leq 1$ for all $i$ and all partial sums $\left(a_{1}, a_{1}+a_{2}\right.$, etc.) are non-negative.

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Source and history

task_id
6de731a7-39bb-5654-987b-a2f076e35f16
task_key
test--6de731a7-39bb-5654-987b-a2f076e35f16
task_revision_id
1
config / split
/ test

Official source

initial import