On automorphisms of certain free nilpotent-by-abelian Lie algebras

For a positive integer Formula: see text, let Formula: see text be a free (nilpotent of class 2)-by-abelian and abelian-by-(nilpotent of class 2) Lie algebra of rank n. We show that the subgroup of Formula: see text generated by the tame automorphisms and a countably infinite set of explicitly given automorphisms of Formula: see text is dense in Formula: see text with respect to the formal power series topology.