I don't understand how to use the Catalan numbers in order to find a path from (0,0) to (x,y) without going over a certain function and while stepping in a specific point. for example:
find the number of paths with length of 16 from (0,0) to (8,8) that are touching the point (3,6) and are under the function: y=x+3
I know that when the problem is from (0,0) to (n,n) and the function is y=x the solution is the n-th catalan number. But what should I do when the function is not y=x or when I have more constraints such as touching a specific point?