# Number of walks on 2D grid

Suppose we are on a finite 2D grid of points from $(0,0)$ to $(a,b)$. Each turn we can move up/down/left/right on this grid (we have 3 possible moves on edges and 2 on corners). In the beginning we are at the point $(x_0,y_0)$ inside the grid. How many ways are there to make $N$ steps on the grid?

I know a recursive solution when the number of ways to make $N$ steps is sum of number of ways to make $N-1$ steps from cell to the left/right/up/down. I wonder is there a combinatorial solution?

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