

A006746


Number of axially symmetric polyominoes with n cells.
(Formerly M1573)


26



0, 0, 0, 1, 2, 6, 9, 23, 38, 90, 147, 341, 564, 1294, 2148, 4896, 8195, 18612, 31349, 70983, 120357, 271921, 463712, 1045559, 1792582, 4034832, 6950579, 15619507, 27023509, 60638559, 105320716, 236006955, 411364068, 920626423, 1609836928
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OFFSET

1,5


COMMENTS

Number of polyominoes with n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid.  Joshua Zucker, Mar 08 2008
The line of reflective symmetry may pass through the center of a square or a vertex of a square. These subsets are enumerated by A349328 and A349329 respectively.  John Mason, Feb 17 2022


REFERENCES

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



CROSSREFS

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328, A349329.


KEYWORD

nonn


AUTHOR



EXTENSIONS

Extended to n=28 by Tomás Oliveira e Silva


STATUS

approved



