By: Nicholas Duchon
I have attached two Flash presentations that I hope help you visualize the recursion in this problem, and help you develop the matrix solution.
The Algorithm (fixed):
int paths (r, c, n)
if (r == n) return 1 // top row
if (c == n) return 1 // right column
return paths (r+1, c, n) + paths (r, c+1, n)
Links to presentation in Flash: