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A351159
Number of polyominoes of n cells with both diagonal symmetries, for which the 180-degree rotational symmetry has an axis that coincides with the center of a square, but without 90-degree rotational symmetry.
2
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 3, 1, 6, 4, 9, 6, 20, 19, 32, 25, 64, 82, 114, 107, 217, 332, 397, 442, 751, 1316
OFFSET
1,11
COMMENTS
This sequence enumerates a subset of the polyominoes enumerated by A056878.
FORMULA
For odd n, a(n) = A056878(n); for even n, a(n) = A056878(n) - A351160(n/2).
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
John Mason, Feb 03 2022
STATUS
approved