  Given a description of the stacking statistics of layered close-packed
structures in the form of a hidden Markov model, we develop analytical
expressions for the pairwise correlation functions between the layers. These
may be calculated analytically as explicit functions of model parameters or the
expressions may be used as a fast, accurate, and efficient way to obtain
numerical values. We present several examples, finding agreement with previous
work as well as deriving new relations.
