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A006747
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Number of rotationally symmetric polyominoes with n cells (that is, polyominoes with exactly the symmetry group C_2 generated by a 180 degree rotation).
(Formerly M3741)
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20
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0, 0, 0, 1, 1, 5, 4, 18, 19, 73, 73, 278, 283, 1076, 1090, 4125, 4183, 15939, 16105, 61628, 62170, 239388, 240907, 932230, 936447, 3641945, 3651618, 14262540
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OFFSET
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1,6
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COMMENTS
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This sequence gives the number of free polyominoes with symmetry group "R", in Redelmeier's notation. See his Tables 1 and 3, also the column "Rot" in Oliveira e Silva's table.
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REFERENCES
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S. W. Golomb, Polyominoes, Princeton Univ. Press, NJ, 1994.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..28.
Tomás Oliveira e Silva, Enumeration of polyominoes
Tomás Oliveira e Silva, Numbers of polyominoes classified according to Redelmeier's symmetry classes (an extract from the previous link)
D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.
D. H. Redelmeier, Table 3 of Counting polyominoes...
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EXAMPLE
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a(2) = 0 because the "domino" polyomino has symmetry group of order 4.
For n=3, the three-celled polyomino [ | | ] has group of order 4, and the polyomino
. [ ]
. [ | ]
has only reflective symmetry, so a(3) = 0.
a(4) = 1 because of (in Golomb's notation) the "skew tetrominoe".
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CROSSREFS
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Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Sequence in context: A190728 A100791 A056883 * A184297 A108412 A205008
Adjacent sequences: A006744 A006745 A006746 * A006748 A006749 A006750
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Extended to n=28 by Tomás Oliveira e Silva
a(1)-a(3) prepended by Andrew Howroyd, Dec 04 2018
Edited by N. J. A. Sloane, Nov 28 2020
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STATUS
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approved
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