We recursively define a sequence $\{ F_{ n,k}\}_{ n,k\in\mathbb N }$ and we prove that such sequence contains only the symbols $\{ 0,1\}.$ We investigate some number-theoretic properties of such sequence and of the way it can be generated. The number $F_n$ can be interpreted as the number of fixed points of semilength $n$ of the map $\gamma$ introduced by Barnabei et al. Our results partially answer conjectures posed by Cori et al.
Categories: math.NT math.CO