Rational interpolation to solutions of Riccati difference equations on elliptic lattices

It is shown how to define difference equations on particular lattices {xn}{xn}, n∈Zn∈Z, where the xnxns are values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations (elliptic Riccati equations) have remarkable simple (!) interpolatory continued fraction expansions.