

A204804


Number of free treelike convex polyominoes with n cells.


0



1, 1, 2, 4, 10, 21, 49, 104, 227, 468, 976, 1978, 4030, 8095, 16313, 32656
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OFFSET

1,3


COMMENTS

Free: none is a rigid transformation (translation, rotation, reflection or glide reflection) of another. Treelike: 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.


LINKS

Table of n, a(n) for n=1..16.
Joseph O'Rourke, MathOverflow Question: Counting restricted polyominoes, July 2011.


EXAMPLE

n=1: one square. n=2: a 2x1 rectangle. n=3: a 3x1 rectangle; an Lshape. So the sequence starts: 1,1,2,... Images up to n=8 at the MathOverflow link.


CROSSREFS

Sequence in context: A128461 A011956 A018003 * A165136 A165137 A065023
Adjacent sequences: A204801 A204802 A204803 * A204805 A204806 A204807


KEYWORD

nonn


AUTHOR

Joseph O'Rourke, Jan 19 2012


EXTENSIONS

a(9)a(16) from Karl Fabian, Jan 22 2012


STATUS

approved



