Ochem's exponential growth conjecture for threshold languages

For every integer $n\geq 2$, let $A_n=\{\texttt{1},\texttt{2},\dots,\texttt{n}\}$ and let $T_n$ be the language of all $\operatorname{RT}(n)^+$-free words over $A_n$, where $\operatorname{RT}(n)$ is the repetition threshold for $n$ letters. Ochem's conjecture. For every $n\geq 3$, the language $T_n$ of threshold words of order $n$ grows exponentially. The case $n=2$ is exceptional: $T_2$ is the language of overlap-free binary words and has polynomial growth. This conjecture has been established for all $n\notin\{12,14,\dots,26\}$ in the source, leaving the listed cases unresolved there.