  We describe a class of fixed polyominoes called $k$-omino towers that are
created by stacking rectangular blocks of size $k\times 1$ 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.
