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A142886
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Number of polyominoes with n cells that have the symmetry group D_8.
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23
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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
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OFFSET
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0,10
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COMMENTS
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This is the largest possible symmetry group that a polyomino can have.
Polyominoes with such symmetry centered about square centers and vertices are enumerated by A351127 and A346800 respectively. - John Mason, Feb 16 2022
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LINKS
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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
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FORMULA
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a(n) = A351127(n) + A346800(n/4) if n is a multiple of 4, otherwise a(n) = A351127(n). - John Mason, Feb 16 2022
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EXAMPLE
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The monomino has eight-fold symmetry. The tetromino with eight-fold symmetry is four cells in a square. The pentomino with eight-fold symmetry is a cell and its four adjacent cells.
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CROSSREFS
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Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351127, A346800.
Sequence in context: A225853 A342128 A330463 * A099026 A341410 A205341
Adjacent sequences: A142883 A142884 A142885 * A142887 A142888 A142889
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 01 2009
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EXTENSIONS
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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
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STATUS
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approved
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