A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function
where is the number of polygons with horizonal bonds, vertical bonds, and area , is not yet known in closed form, but it can be evaluated in polynomial time (Conway et al. 1997, Bousquet-Mélou 1999). The perimeter-generating function has a logarithmic singularity and so is not algebraic, but is known to be D-finite (Conway et al. 1997, Bousquet-Mélou 1999).
The anisotropic area and perimeter generating function satisfies an inversion relation of the form
(Bousquet-Mélou et al. 1999).