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).
A new way of counting the column-convex polyominoes by perimeter.Discrete Mathematics
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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).