  In this paper we study the smallest Mealy automaton of intermediate growth,
first considered by the last two authors. We describe the automatic
transformation monoid it defines, give a formula for the generating series for
its (ball volume) growth function, and give sharp asymptotics for its growth
function, namely [ F(n) \sim 2^{5/2} 3^{3/4} \pi^{-2} n^{1/4}
\exp{\pi\sqrt{n/6}} ] with the ratios of left- to right-hand side tending to 1
as $n \to \infty$.
