  Column-convex polygons were first counted by area several decades ago, and
the result was found to be a simple, rational, generating function. In this
chapter we generalize that result. Let a p-column polyomino be a polyomino
whose columns can have 1, 2,..., p connected components. Then column-convex
polygons are equivalent to 1-convex polyominoes. The area generating function
of even the simplest generalization, namely to 2-column polyominoes, is
unlikely to be solvable. We therefore define a class of polyominoes which
interpolates between column-convex polygons and 2-column polyominoes. We derive
the area generating function of that class, using an extension of an existing
algorithm. The growth constant of the new class is greater than the growth
constant of column-convex polygons. A rather tight lower bound on the growth
constant complements a compelling numerical analysis.
