  Combinatorics of biopolymer structures, especially enumeration of various RNA
secondary structures and protein contact maps, is of significant interest for
communities of both combinatorics and computational biology. However, most of
the previous combinatorial enumeration results for these structures are
presented in terms of generating functions, and few are explicit formulas. This
paper is mainly concerned with finding explicit enumeration formulas for a
particular class of biologically relevant structures, say, saturated 2-regular
simple stacks, whose configuration is related to protein folds in the 2D
honeycomb lattice. We establish a semi-bijective algorithm that converts
saturated 2-regular simple stacks into forests of small trees, which produces a
uniform formula for saturated extended 2-regular simple stacks with any of the
six primary component types. Summarizing the six different primary component
types, we obtain a bivariate explicit formula for saturated extended 2-regular
simple stacks with $n$ vertices and $k$ arcs. As consequences, the uniform
formula can be reduced to Clote's results on $k$-saturated 2-regular simple
stacks and the optimal 2-regular simple stacks, and Guo et al.'s result on the
optimal extended 2-regular simple stacks.
