

A006747


Number of rotationally symmetric polyominoes with n cells (that is, polyominoes with exactly the symmetry group C_2 generated by a 180degree rotation).
(Formerly M3741)


27



0, 0, 0, 1, 1, 5, 4, 18, 19, 73, 73, 278, 283, 1076, 1090, 4125, 4183, 15939, 16105, 61628, 62170, 239388, 240907, 932230, 936447, 3641945, 3651618, 14262540, 14277519, 55987858, 55961118, 220223982, 219813564, 867835023, 865091976, 3425442681
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OFFSET

1,6


COMMENTS

This sequence gives the number of free polyominoes with symmetry group "R" in Redelmeier's notation. See his Tables 1 and 3, also the column "Rot" in Oliveira e Silva's table.
Polyominoes having this symmetry may have an axis of symmetry that coincides with the center of a square, the middle of an edge, or a vertex of a square. These subsets are enumerated by A351615, A234008 and A351616 respectively.  John Mason, Feb 17 2022


REFERENCES

S. W. Golomb, Polyominoes, Princeton Univ. Press, NJ, 1994.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

D. H. Redelmeier, Table 3 of Counting polyominoes...


FORMULA



EXAMPLE

a(2) = 0 because the "domino" polyomino has symmetry group of order 4.
For n=3, the threecelled polyomino [   ] has group of order 4, and the polyomino
. [ ]
. [  ]
has only reflective symmetry, so a(3) = 0.
a(4) = 1 because of (in Golomb's notation) the "skew tetromino".


CROSSREFS

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351615, A234008, A351616.


KEYWORD

nonn


AUTHOR



EXTENSIONS

Extended to n=28 by Tomás Oliveira e Silva


STATUS

approved



