On the 3-state Mealy automata over an m-symbol alphabet of growth order [nlogn/2logm]

We consider sequence of 3-state Mealy automata over an m-symbol alphabet such that the growth of Jm is intermediate of order [nlogn/2logm]. For each automaton Jm we describe the transformation monoid SJm, defined by it, provide generating series for the growth functions, and consider some properties of SJm and Jm.