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Find an expression for $x_n$ if sequence $\{x_n\}$ satisfies $x_1=2$, $x_2=3$, and $$\left\{ \begin{array}{ccll} x_{2k+1}&=&x_{2k} +x_{2k-1}&\quad (k\ge 1)\\ x_{2k}&=&x_{2k-1} + 2x_{2k-2}&\quad (k\ge 2) \end{array} \right.$$