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