MathNet 2013 Question 5

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