

A006747


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


20



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
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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.


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

Table of n, a(n) for n=1..28.
Tomás Oliveira e Silva, Enumeration of polyominoes
Tomás Oliveira e Silva, Numbers of polyominoes classified according to Redelmeier's symmetry classes (an extract from the previous link)
D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191203.
D. H. Redelmeier, Table 3 of Counting polyominoes...


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 tetrominoe".


CROSSREFS

Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
Sequence in context: A190728 A100791 A056883 * A184297 A108412 A205008
Adjacent sequences: A006744 A006745 A006746 * A006748 A006749 A006750


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Extended to n=28 by Tomás Oliveira e Silva
a(1)a(3) prepended by Andrew Howroyd, Dec 04 2018
Edited by N. J. A. Sloane, Nov 28 2020


STATUS

approved



