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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
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
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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)