Question 50
We consider points with integer coordinates in the rectangle with corners in $(0,0)$, $(n,0)$, $(n,2)$ and $(0,2)$. It is possible to move from a point $(a,b)$ in the rectangle to either points $(a+1,b)$, $(a+1,b+1)$ or $(a,b-1)$ if the second point is also in the given rectangle.
How many possible paths are there from $(0,0)$ to $(n,2)$ under these rules?
How many possible paths are there from $(0,0)$ to $(n,2)$ under these rules?