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Hex-trees are identified as a particular instance of weighted unary-binarytrees. The Horton-Strahler numbers of these objects are revisited, and, thanksto a substitution that is not immediately intuitive, explicit results arepossible. 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 sequenceA002212 in the Encyclopedia of integer sequences.

Weighted unary-binary trees, Hex-trees, marked ordered trees, and related structures