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A006749
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Number of asymmetric polyominoes with n cells.
(Formerly M3906)
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26
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0, 0, 0, 1, 5, 20, 84, 316, 1196, 4461, 16750, 62878, 237394, 899265, 3422111, 13069026, 50091095, 192583152, 742560511, 2870523142, 11122817672, 43191285751, 168046076423, 654997492842, 2557223459805, 9999080270766, 39152997087077, 153511067364760
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OFFSET
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1,5
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COMMENTS
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This sequence counts polyominoes whose symmetry group has order 1.
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REFERENCES
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A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen. 28(1995) 891-904.
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
T. R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967) and accompanying letter from T. J. Lander (annotated scanned copy). See page 21.
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) + A259090(n) = A000105(n). - R. J. Mathar, Sep 29 2021
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CROSSREFS
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Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749, A006884, A006885, A006877, A006878, A033492.
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Sequence in context: A292760 A270322 A056884 * A002213 A099949 A006231
Adjacent sequences: A006746 A006747 A006748 * A006750 A006751 A006752
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KEYWORD
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nonn,nice
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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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