Another kind of geometric path in the plane is a diagonal lattice path. Such a path is a path made up of line segments that go from a point (i, j) to (i 1, j 1) (this is often called an upstep) or (i 1, j 1) (this is often called a downstep), again where i and j are integers. (Thus diagonal lattice paths always move towards the right but may move up or down.) Required:
a. List all the diagonal lattice paths from (0,0) to (4,0).
b. Describe which points can be reached from (0,0) by diagonal lattice paths.
c. What is the length (i. e., the number of steps) of a diagonal lattice path from (0,0) to (m, n)?
d. Assuming that (m, n) is such a point, how many diagonal lattice paths are there from (0,0) to (m, n)?