Let at t=0 a drunkard be at x = 0
At each time interval he jumps +/- 1. So at t=1 he is at x = -1 OR at x = 1.
Given that at t = 2n , dunkard is back at x = 0.
So number of possible paths are
1. Of the above possible paths, how many paths are there such that the drunkard is always within 'a' units from the origin. i.e. |x|<=a for all t = 0,1,2,....2n.
Note: I was able to solve the case where instead of |x|<=a, we just had x<=a. (Using the reflection principle). But with |x| I don't seem to be getting anywhere
Any help here please?