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Omni-MATH / Find the number of sequences a₁,a₂,…,a₁₀ of positive integers with the property that a_(n+2)=a_(n+1)+a_(n) for n=1,2,…,8, and a₁₀=2002.

Problem

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problem

Find the number of sequences a1,a2,…,a10a_{1}, a_{2}, \ldots, a_{10} of positive integers with the property that an+2=an+1+ana_{n+2}=a_{n+1}+a_{n} for n=1,2,…,8n=1,2, \ldots, 8, and a10=2002a_{10}=2002.
Plain-text mathematical notation (without MathML)
Find the number of sequences a₁,a₂,…,a₁₀ of positive integers with the property that a_(n+2)=a_(n+1)+a_(n) for n=1,2,…,8, and a₁₀=2002.
Original LaTeX notation
Find the number of sequences $a_{1}, a_{2}, \ldots, a_{10}$ of positive integers with the property that $a_{n+2}=a_{n+1}+a_{n}$ for $n=1,2, \ldots, 8$, and $a_{10}=2002$.

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Source and history

task_id
09fc3981-cc4a-5656-bc44-5f8b06d53add
task_key
test--09fc3981-cc4a-5656-bc44-5f8b06d53add
task_revision_id
1
config / split
/ test

Official source

initial import