login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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), 191-203.

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 three-celled 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)