  Hex-trees are identified as a particular instance of weighted unary-binary
trees. The Horton-Strahler numbers of these objects are revisited, and, thanks
to a substitution that is not immediately intuitive, explicit results are
possible. They are augmented by asymptotic evaluations as well. Furthermore,
marked ordered trees (in bijection to skew Dyck paths) are investigated,
followed 3-Motzkin paths and multi-edge trees. The underlying theme is sequence
A002212 in the Encyclopedia of integer sequences.
