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A142886 Number of polyominoes with n cells that have the symmetry group D_4. 18
1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 3, 2, 0, 0, 5, 4, 0, 0, 12, 7, 0, 0, 20, 11, 0, 0, 45, 20, 0, 0, 80, 36, 0, 0, 173, 65, 0, 0, 310, 117, 0, 0, 664, 216, 0, 0, 1210, 396, 0, 0, 2570, 736, 0, 0, 4728, 1369, 0, 0, 9976, 2558, 0, 0, 18468, 4787 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

This is the largest possible symmetry group that a polyomino can have.

LINKS

Robert A. Russell, Table of n, a(n) for n = 0..163

Tomás Oliveira e Silva, Enumeration of polyominoes

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

D. H. Redelmeier, Table 3 of Counting polyominoes...

Index entries for sequences related to groups

EXAMPLE

The monomino has eightfold symmetry. The tetromino with eightfold symmetry is four cells in a square. The pentomino with eightfold symmetry is a cell and its four adjacent cells.

CROSSREFS

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.

Sequence in context: A259827 A143161 A225853 * A099026 A205341 A195664

Adjacent sequences:  A142883 A142884 A142885 * A142887 A142888 A142889

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 01 2009

EXTENSIONS

Name corrected by Wesley Prosser, Sep 06 2017

a(28) added by Andrew Howroyd, Dec 04 2018

More terms from Robert A. Russell, Jan 13 2019

STATUS

approved

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Last modified October 17 23:33 EDT 2019. Contains 328135 sequences. (Running on oeis4.)