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.

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

Author

John Mason, Feb 03 2022

Keywords

• nonn
• more

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056878.

Examples

			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

Cf. A000105, A056878, A351160.

Formula

For odd n, a(n) = A056878(n); for even n, a(n) = A056878(n) - A351160(n/2).