A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis as in the example illustrated which shows 8 steps? How many paths are there for 4 steps, for 6 steps, for 8 steps? Draw the paths on a diagram. Compare your answers to the values of
 1

2
(3[(n − 2)/2] + 1 )

where n=2,4,6,8. What about n = 10?