Let be the set of -lattice path which begin at , do not use the same vertex twice, and never touch either the -axis or the -axis. Determine the largest value of such that every path in which ends at has length at most .
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 to is .
The length of a lattice path is the number of steps in the path.
For a set , an -lattice path is a lattice path where every step has size which is a member of .