Fibonacci transition-graph cycle count
= Fibonacci transition-graph cycle count
A period-three orbit forces an interval-covering graph with adjacency matrix
$$
A=\begin{pmatrix}1&1\\1&0\end{pmatrix}.
$$
Its number of closed pointed length-$n$ itineraries is $\operatorname{tr}(A^n)=L_n$. Möbius removal of lower periods and division by $n$ give four primitive cyclic classes at $n=7$ and five at $n=8$.