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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 work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, . . . , p connected components. Then columnconvex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define twodoi:10.1088/1751-8113/42/48/485003 fatcat:kjmzkqfvvrf2phxyalsgycn6py