Given you an infinite 2-dimensional plane, and find all paths from (0,0) to (2n,0) with some limitation factors:
1.You cannot step to points that under the y-axis.
2.For every step you can perform one of the following operations:
(1) move right for 2 steps, e.g. from (x, y) to (x+2, y)
(2) move right, then move up, e.g. from (x, y) to (x+1, y+1)
(3) move right, then move down, e.g. from (x, y) to (x+1, y-1)
Now you must find out the numbers of different operation sequences.