Quiddity sequences for $\mathrm{SL}_3$-frieze patterns

The notion of a $(k,n)$-frieze pattern was introduced by the author as a generalisation of the classical frieze patterns. In this article we describe connections between classes of $(3,n)$-frieze patterns and classes of $\mathrm{SL}_3$-frieze patterns. We introduce the idea of a superimposed triangulation and clarify how superimposed triangulations may be used to understand quiddity sequences for $\mathrm{SL}_3$-frieze patterns.