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Omni-MATH / Let a₁,a₂,… be a sequence of positive integers such that for integers n>2,a_(n)= 3a_(n−1)−2a_(n−2). How many such sequences {a_(n)} are there such that a₂₀₁₀≤2²⁰¹² ?

Problem

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problem

Let a1,a2,…a_{1}, a_{2}, \ldots be a sequence of positive integers such that for integers n>2,an=n>2, a_{n}= 3an−1−2an−23 a_{n-1}-2 a_{n-2}. How many such sequences {an}\left\{a_{n}\right\} are there such that a2010≤22012a_{2010} \leq 2^{2012} ?
Plain-text mathematical notation (without MathML)
Let a₁,a₂,… be a sequence of positive integers such that for integers n>2,a_(n)= 3a_(n−1)−2a_(n−2). How many such sequences {a_(n)} are there such that a₂₀₁₀≤2²⁰¹² ?
Original LaTeX notation
Let $a_{1}, a_{2}, \ldots$ be a sequence of positive integers such that for integers $n>2, a_{n}=$ $3 a_{n-1}-2 a_{n-2}$. How many such sequences $\left\{a_{n}\right\}$ are there such that $a_{2010} \leq 2^{2012}$ ?

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Source and history

task_id
6fbc5e28-b713-56e2-bf37-34849c2c4c26
task_key
test--6fbc5e28-b713-56e2-bf37-34849c2c4c26
task_revision_id
1
config / split
/ test

Official source

initial import