  We study the thermodynamic formalism for particular types of sub-additive
sequences on a class of subshifts over countable alphabets. The subshifts we
consider include factors of irreducible countable Markov shifts under certain
conditions. We show the variational principle for topological pressure. We also
study conditions for the existence and uniqueness of invariant ergodic Gibbs
measures and the uniqueness of equilibrium states. As an application, we extend
the theory of factors of (generalized) Gibbs measures on subshifts on finite
alphabets to that on certain subshifts over countable alphabets.
