Entropy of dimers chains placed on a one-dimensional lattice with q-states

We calculate the entropy of a chain of dimers placed on a one-dimensional lattice as a function of the density of monomers. We consider Np dimer chains with a number of monomers M=2 which may assume q-states (orientations) on the one-dimensional lattice. In this work we treated a simple model which has exact solutions both in the micro-canonical and grand-canonical formalisms. The analytic result in the micro-canonical and grand-canonical ensembles were successfully confirmed by a Monte Carlo algorithm.