In a rectangular grid point (i, j) with nonnegative integer coordinates, a diagonal lattice path is made of line segments that go from a point (i, j) to (i + 1, j +1) or (i + 1, j - 1). Thus, diagonal...

In a rectangular grid point(i, j)with nonnegative integer coordinates, a diagonal lattice path is made of line segments that go from a point(i, j)to(i + 1, j +1)or(i + 1, j - 1). Thus, diagonal lattice paths always move towards the right, but may move up or down; no horizontal or vertical steps involved.

1. Which points on the grid are connected to (0, 0) by the diagonal lattice paths?

2. If (0, 0) is connected to (m, n) by the diagonal lattice path, then how many such paths are there? Prove your claim.