HMMT November 2013 T8

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Define the sequence $\left\{x_{i}\right\}_{i \geq 0}$ by $x_{0}=x_{1}=x_{2}=1$ and $x_{k}=\frac{x_{k-1}+x_{k-2}+1}{x_{k-3}}$ for $k>2$ . Find $x_{2013}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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