  An RNA secondary structure is designable if there is an RNA sequence which
can attain its maximum number of base pairs only by adopting that structure.
The combinatorial RNA design problem, introduced by Hale\v{s} et al. in 2016,
is to determine whether or not a given RNA secondary structure is designable.
Hale\v{s} et al. identified certain classes of designable and non-designable
secondary structures by reference to their corresponding rooted trees. We
introduce an infinite class of rooted trees containing unpaired nucleotides at
the greatest depth, and prove constructively that their corresponding secondary
structures are designable. This complements previous results for the
combinatorial RNA design problem.
