  Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix
positive integers r,s and put an equivalence relation on points of Z^2 by
letting v,w be equivalent if v - w = m (r,s) for some m in Z. Call a lattice
path valid if whenever it enters a point v with an E-step, then any further
points of the path in the class of v are also entered with an E-step. Loehr and
Warrington conjectured that the number of valid paths from (0,0) to (nr,ns) is
(r+s choose r)^n. We prove this conjecture when s = 2.
