On the density of certain languages with $p^2$ letters

Carlos Segovia, Monika Winklmeier

The sequence $(x_n{)}_{n\in \mathbb{N}}=(2,5,15,51,187,\dots )$ given by the rule $x_n=(2^n+1)(2^{n-1}+1)/3$ appears in several seemingly unrelated areas of mathematics. For example,…