Row-convex polyominoes without holes are counted by summing permutation products over integer partitions of the area, producing a generating function whose asymptotics involve 2^N scaled by a cosine oscillation at angle arctan(sqrt(7)/3).
Checker boards and polyominoes.The American Mathematical Monthly.61, 675-682 (1954)
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A Partition-Based Generating Function for Row-Convex Polyominoes
Row-convex polyominoes without holes are counted by summing permutation products over integer partitions of the area, producing a generating function whose asymptotics involve 2^N scaled by a cosine oscillation at angle arctan(sqrt(7)/3).