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A006748
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Number of diagonally symmetric polyominoes with n cells.
(Formerly M0366)
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25
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0, 0, 1, 0, 2, 2, 7, 5, 26, 22, 91, 79, 326, 301, 1186, 1117, 4352, 4212, 16119, 15849, 60174, 60089, 226146, 228426, 854803, 872404, 3247207, 3342579, 12389106, 12850662, 47448984, 49544820, 182338754, 191529007, 702807040, 742163178, 2716205709, 2882119756
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OFFSET
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1,5
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COMMENTS
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This sequence counts polyominoes with exactly the symmetry group of order 2 generated by a single reflection about a diagonal.
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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 (terms up to a(47) from Robert A. Russell)
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...
Toshihiro Shirakawa, Harmonic Magic Square, pp 3-4: Enumeration of Polyominoes considering the symmetry, April 2012.
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FORMULA
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a(n) = (A346800(n) - A142886(n)) / 2 - A056878(n). - Robert A. Russell, Aug 25 2021
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CROSSREFS
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Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747.
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Sequence in context: A223000 A058625 A300126 * A193548 A131049 A126851
Adjacent sequences: A006745 A006746 A006747 * A006749 A006750 A006751
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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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