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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 (list; graph; refs; listen; history; text; internal format)
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
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...
FORMULA
a(n) = A349328(n) + A349329(n/2) for even n, otherwise a(n) = A349328(n). - John Mason, Feb 17 2022
CROSSREFS
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328, A349329.
Sequence in context: A346673 A077237 A056879 * A205875 A243558 A244427
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended to n=28 by Tomás Oliveira e Silva
STATUS
approved

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Last modified February 28 04:16 EST 2024. Contains 370379 sequences. (Running on oeis4.)