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A056878
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Number of polyominoes with n cells, symmetric about diagonal 2.
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26
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0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 3, 3, 5, 6, 14, 9, 20, 20, 56, 32, 80, 64, 224, 114, 315, 217, 863, 397, 1234, 751, 3331, 1400, 4816, 2632, 12815, 4973, 18792, 9349, 49400, 17810, 73338, 33557, 190643, 64309, 286368, 121511, 737532, 233891, 1119215, 443271, 2859154
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OFFSET
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1,11
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COMMENTS
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The sequence refers to those polyominoes having reflective symmetry on both diagonals, consequent 180-degree rotational symmetry, but without 90-degree rotational symmetry. Such polyominoes with rotational symmetry symmetry centered about square centers and vertices are enumerated by A351159 and A351160 respectively. - John Mason, Feb 17 2022
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LINKS
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Robert A. Russell, Table of n, a(n) for n = 1..87
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) = A351159(n) + A351160(n/2) for even n, otherwise a(n) = A351159(n). - John Mason, Feb 17 2022
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EXAMPLE
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For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common. For a(8)=1, the octomino is composed of a 2 X 2 square and the four cells adjacent to two nonadjacent cells of that square.
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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, A351159, A351160.
Sequence in context: A121400 A238003 A218932 * A270520 A092557 A333295
Adjacent sequences: A056875 A056876 A056877 * A056879 A056880 A056881
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Sep 03 2000
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EXTENSIONS
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More terms from Robert A. Russell, Jan 18 2019
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STATUS
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approved
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