The Zeta function, Periodic Points and Entropies of the Motzkin Shift
  We discuss a method of calculating the zeta function of subshifts which have a presentation by a finite directed graph labeled by elements of the associated inverse semigroup. This class of subshifts is introduced as a class of property A subshifts(T.Hamachi, K.Inoue and W.Krieger/Subsystems of finite type and semigroup invariants of subshifts, preprint), and the Dyck shift and the Motzkin shift are representative subshifts in this class. The exact number of the periodic points and entropies are also given by this method, and these values are used in the embedding condition for an irreducible shift of finite type into a subshift in this class. 
Kokoro Inoue