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 A142886 Number of polyominoes with n cells that have the symmetry group D_8. 23
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS 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 LINKS 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... FORMULA a(n) = A351127(n) + A346800(n/4) if n is a multiple of 4, otherwise a(n) = A351127(n). - John Mason, Feb 16 2022 EXAMPLE 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. CROSSREFS 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 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 01 2009 EXTENSIONS 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 STATUS approved

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Last modified June 29 07:33 EDT 2022. Contains 354910 sequences. (Running on oeis4.)