Posted by **doeom** on Sunday, June 30, 2013 at 9:04pm.

Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the x-axis or the y-axis.

Let Px,y be the number of paths in S which end at the point (x,y). Determine P2,4.

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).

The length of a lattice path is the number of steps in the path.

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.

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