  In this paper, we generalize 2-trees by replacing triangles by
quadrilaterals, pentagons or $k$-sided polygons ($k$-gons), where $k\geq 3$ is
fixed. This generalization, to $k$-gonal 2-trees, is natural and is closely
related, in the planar case, to some specializations of the cell-growth
problem. Our goal is the labelled and unlabelled enumeration of $k$-gonal
2-trees according to the number $n$ of $k$-gons. We give explicit formulas in
the labelled case, and, in the unlabelled case, recursive and asymptotic
formulas.
