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A144553
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Number of polyominoes with n cells that have precisely the symmetry group of order 4 generated by 90-degree rotations.
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22
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0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 0, 12, 7, 0, 0, 44, 25, 0, 0, 165, 90, 0, 0, 603, 319, 0, 0, 2235, 1136, 0, 0, 8283, 4088, 0, 0, 30936, 14868, 0, 0, 116096, 54526, 0, 0, 438463, 201527, 0, 0, 1663701, 750169, 0, 0, 6342086, 2809931, 0, 0
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,12
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COMMENTS
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The values for n>28 were produced by a set of programs, the most difficult of which is attached. There is no guarantee that the values are correct, although presumably Shirakawa has calculated them through a(45). The attached program can be altered to count only achiral polyominoes, and those results match those of A142886, which uses a very different method. The difficulties lie in determining each inner loop (A324408 and A324409) and in determining connections within the inner loop (bad_connection subroutine). The last bug I found in the program affected only polyominoes with 72 or more cells. - Robert A. Russell, May 23 2020
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LINKS
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Robert A. Russell, Table of n, a(n) for n = 1..91
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...
Robert A. Russell, C++ Program
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FORMULA
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a(n) = A030228(n) - A006747(n) - A006749(n). - Jean-François Alcover, Sep 09 2019, after Andrew Howroyd in A030228.
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MATHEMATICA
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A006747 = Cases[Import["https://oeis.org/A006747/b006747.txt",
"Table"], {_, _}][[All, 2]];
A006749 = Cases[Import["https://oeis.org/A006749/b006749.txt",
"Table"], {_, _}][[All, 2]];
A030228 = Cases[Import["https://oeis.org/A030228/b030228.txt",
"Table"], {_, _}][[All, 2]];
a[n_] := A030228[[n]] - A006747[[n]] - A006749[[n]];
Array[a, 28] (* Jean-François Alcover, Sep 09 2019 *)
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CROSSREFS
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Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Cf. A324408, A324409 (inner rings).
Sequence in context: A246159 A059033 A133209 * A187130 A187145 A285700
Adjacent sequences: A144550 A144551 A144552 * A144554 A144555 A144556
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane, Jan 01 2009
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EXTENSIONS
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a(28) added by Andrew Howroyd, Dec 04 2018
a(29)-a(91) added by Robert A. Russell, May 23 2020
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STATUS
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approved
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