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%I #23 May 06 2021 10:27:19
%S 1,1,2,4,10,21,49,104,227,468,976,1978,4030,8095,16313,32656,65503,
%T 130986
%N Number of free tree-like convex polyominoes with n cells.
%C Free: none is a rigid transformation (translation, rotation, reflection or glide reflection) of another. Tree-like: never does a 2x2 subarrangement of squares occur in the shape. So the dual graph is a tree. Convex: every horizontal, or vertical line, meets the shape in either a single segment, or not at all.
%H Joseph O'Rourke, <a href="http://mathoverflow.net/questions/71032/">MathOverflow Question: Counting restricted polyominoes</a>, July 2011.
%e n=1: one square. n=2: a 2x1 rectangle. n=3: a 3x1 rectangle; an L-shape. So the sequence starts: 1,1,2,... Images up to n=8 at the MathOverflow link.
%K nonn,hard,more
%O 1,3
%A _Joseph O'Rourke_, Jan 19 2012
%E a(9)-a(16) from _Karl Fabian_, Jan 22 2012
%E a(17)-a(18) from _John Mason_, May 06 2021