Question

How many {(1,1),(1,−1),(2,0)}-lattice paths are there from the point (0,0) to the line x=8?
Details and assumptions
A lattice path is a path in the Cartesian plane between points with integer coordinates.

A step in a lattice path is a single move from one point with integer coordinates to another.

The size of the step from (x1,y1) to (x2,y2) is (x2−x1,y2−y1).

For a set S={(xi,yi)}ki=1, an S-lattice path is a lattice path where every step has size which is a member of S.