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 A144554 Number of polyominoes with n cells whose symmetry group (excluding reflections) has order at least 2. 12
 1, 1, 1, 3, 3, 7, 8, 25, 25, 82, 85, 302, 307, 1111, 1131, 4216, 4267, 16076, 16253, 61976, 62475, 239927, 241447, 933576, 937574, 3644073, 3653624, 14267757, 14281711, 55996279, 55968648, 220244340, 219829297, 867868410, 865120447, 3425522409, 3410557920, 13540713898, 13466370893, 53596553368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In other words, a(n) is the number of polyominoes with n cells having at least 180-degree rotational symmetry. - John Mason, Feb 14 2022 LINKS John Mason, Table of n, a(n) for n = 1..50 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 This is the sum of A142886, A056877, A144553, A056878 and A006747. - Joseph Myers, Dec 31 2008 a(n) = A000105(n) - A006749(n) - A006746(n) - A006748(n). - John Mason, Feb 14 2022 MATHEMATICA A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]]; A006749 = Cases[Import["https://oeis.org/A006749/b006749.txt", "Table"], {_, _}][[All, 2]]; A006746 = Cases[Import["https://oeis.org/A006746/b006746.txt", "Table"], {_, _}][[All, 2]]; A006748 = Cases[Import["https://oeis.org/A006748/b006748.txt", "Table"], {_, _}][[All, 2]]; a[n_] := A000105[[n+1]] - A006749[[n]] - A006746[[n]] - A006748[[n]]; Table[a[n], {n, 1, 48}] (* Jean-François Alcover, Aug 17 2022 *) CROSSREFS Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554. Sequence in context: A056357 A288728 A213942 * A177936 A337975 A143088 Adjacent sequences: A144551 A144552 A144553 * A144555 A144556 A144557 KEYWORD nonn AUTHOR Fred Schneider, Dec 28 2008 EXTENSIONS Edited by N. J. A. Sloane, Jan 01 2009 17 additional terms (just summing the terms from the 5 sequences specified in the description) Fred Schneider, Jan 03 2009 a(28) from John Mason, Oct 05 2021 a(29)-a(36) from John Mason, Oct 16 2021 Terms a(37) and beyond from John Mason, Feb 14 2022 STATUS approved

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Last modified November 29 06:00 EST 2023. Contains 367422 sequences. (Running on oeis4.)