We consider the sequence ${ J_m,m \ge 2}$ of the 3-state Mealy automata over an m-symbol alphabet such that the growth function of $J_m$ has the intermediate growth order $[n ^{ { \log n}/{ 2 \log m}} ]$. For each automaton $J_m$ we describe the automaton transformation monoid $S_{ J_m}$, defined by it, provide generating series for the growth functions, and consider primary properties of $S_{ J_m}$ and $J_m$.
Categories: math.AG math.CO