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A204804 Number of free tree-like convex polyominoes with n cells. 0
1, 1, 2, 4, 10, 21, 49, 104, 227, 468, 976, 1978, 4030, 8095, 16313, 32656 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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 L-shape. 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

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Last modified July 24 04:31 EDT 2014. Contains 244874 sequences.