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A006746
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Number of axially symmetric polyominoes with n cells.
(Formerly M1573)
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26
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0, 0, 0, 1, 2, 6, 9, 23, 38, 90, 147, 341, 564, 1294, 2148, 4896, 8195, 18612, 31349, 70983, 120357, 271921, 463712, 1045559, 1792582, 4034832, 6950579, 15619507, 27023509, 60638559, 105320716, 236006955, 411364068, 920626423, 1609836928
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OFFSET
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1,5
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COMMENTS
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Number of polyominoes with n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid. - Joshua Zucker, Mar 08 2008
The line of reflective symmetry may pass through the center of a square or a vertex of a square. These subsets are enumerated by A349328 and A349329 respectively. - John Mason, Feb 17 2022
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REFERENCES
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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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John Mason, Table of n, a(n) for n = 1..48
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...
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FORMULA
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a(n) = A349328(n) + A349329(n/2) for even n, otherwise a(n) = A349328(n). - John Mason, Feb 17 2022
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CROSSREFS
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Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749, A030227.
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328, A349329.
Sequence in context: A346673 A077237 A056879 * A205875 A243558 A244427
Adjacent sequences: A006743 A006744 A006745 * A006747 A006748 A006749
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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
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STATUS
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approved
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