  We first enumerate a generalization of domino towers that was proposed by
Tricia M. Brown (J. Integer Seq. 20 (2017)), which we call S-omino towers. We
establish equations that the generating function must satisfy and then apply
the Lagrange inversion formula to find a closed formula for the number of
towers. We also show a connection to generalized Dyck paths and provide an
explicit bijection. Finally, we consider the set of row-convex k-omino towers,
introduced by Brown, and calculate an exact generating function.
