On the enumeration of k-omino towers

We describe a class of fixed polyominoes called k-omino towers that are created by stacking rectangular blocks of size k×1 on a convex base composed of these same k-omino blocks. By applying a partition to the set of k-omino towers of fixed area kn, we give a recurrence on the k-omino towers therefore showing the set of k-omino towers is enumerated by a Gauss hypergeometric function. The proof in this case implies a more general hypergeometric identity with parameters similar to those given in a classical result of Kummer.