Knight Movement I

A knight in chess can move $(\pm 2, \pm 1)$ or $(\pm 1, \pm 2)$ at each turn, as long as that movement stays inside the board. The chess starts at $(1,1)$ in an $n\times n$ chess board (bottom left corner), where $n \geq 6$ and $n \equiv 1$ mod $3$. Find the number of shortest paths from $(1,1)$ to $(n,n)$ when $n = 13$.