Enumeration of various animals on the triangular lattice

In this paper, we consider various classes of polyiamonds that are animals residing on the triangular lattice. By careful analyses through certain layer-by-layer decompositions and cell pruning/growing arguments, derive explicit forms for generating functions number nonempty translation-invariant baryiamonds (bargraphs in lattice), column-convex polyiamonds, convex with respect to their perimeter. particular, show (A) perimeter n asymptotically (?+1)2?4+?3?2?+12?n3??n?2,where ? is a root polynomial degree 5. (B) asymptotic (1799780917+33?13?175463)9517?11927?432?8926?n33+172n?1. (C) 12804413?n33n.