  We show that the generating function (in n) for the number of walks on the
square lattice with steps (1,1), (1,-1), (2,2) and (2,-2) from (0,0) to (2n,0)
in the region 0 <= y <= w satisfies a very special fifth order nonlinear
recurrence relation in w that implies both its numerator and denominator
satisfy a linear recurrence relation.
