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A056878 Number of polyominoes with n cells, symmetric about diagonal 2. 26
0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 3, 3, 5, 6, 14, 9, 20, 20, 56, 32, 80, 64, 224, 114, 315, 217, 863, 397, 1234, 751, 3331, 1400, 4816, 2632, 12815, 4973, 18792, 9349, 49400, 17810, 73338, 33557, 190643, 64309, 286368, 121511, 737532, 233891, 1119215, 443271, 2859154 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
COMMENTS
The sequence refers to those polyominoes having reflective symmetry on both diagonals, consequent 180-degree rotational symmetry, but without 90-degree rotational symmetry. Such polyominoes with rotational symmetry symmetry centered about square centers and vertices are enumerated by A351159 and A351160 respectively. - John Mason, Feb 17 2022
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) = A351159(n) + A351160(n/2) for even n, otherwise a(n) = A351159(n). - John Mason, Feb 17 2022
EXAMPLE
For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common. For a(8)=1, the octomino is composed of a 2 X 2 square and the four cells adjacent to two nonadjacent cells of that square.
CROSSREFS
Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351159, A351160.
Sequence in context: A121400 A238003 A218932 * A270520 A092557 A333295
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 03 2000
EXTENSIONS
More terms from Robert A. Russell, Jan 18 2019
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)