$cache={}
def robot(width,height,x=0,y=0)
    return 1 if x == width-1 and y == height-1 # We reached the Finish, 1 solution found
    return $cache[[width,height,x,y]] if $cache[[width,height,x,y]] # Did we already computed the solution for this square? Just return it instead of recompute.
    solutions = 0
    solutions += robot(width,height,x+1,y) if x != width-1 # The number of solutions starting from the current square (x,y) are all the solutions starting at x+1,y (if it is valid to move on the right)
    solutions += robot(width,height,x,y+1) if y != height-1 # Plus the solutions starting at x,y+1 (if it is valid to move on the bottom)
    $cache[[width,height,x,y]] = solutions # Save the solution for this square
    return solutions
end
puts(robot(31,43))