  In this note we consider several kind of partition functions of
one-dimensional models with nearest - neighbor interactions $I_n, n\in
\mathbf{Z}$ and spin values $\pm 1$. We derive systems of recursive equations
for each kind of such functions. These systems depend on parameters $I_n, n\in
\mathbf{Z}$. Under some conditions on the parameters we describe solutions of
the systems of recursive equations.
