A351191 Number of polyominoes of 4n cells with both horizontal and vertical symmetries, for which the 180-degree rotational symmetry has an axis that coincides with a vertex of a square of the underlying matrix, but without 90-degree rotational symmetry.

0, 1, 2, 9, 29, 106, 372, 1356, 4928, 18200, 67541, 252847, 951615, 3602131, 13696141, 52295335, 200393559, 770406039, 2970353199, 11482373919, 44491696182, 172766226170, 672185941552, 2619994156474, 10228900153083, 39996337310835, 156612012801698

Offset: 1

Author

John Mason, Feb 05 2022

Keywords

• nonn

Comments

This sequence enumerates a subset of the polyominoes enumerated by A056877.

Examples

			a(2)=1 because of the 2 by 4 octomino.
		

Links

• John Mason, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000105, A056877, A144553, A006747, A006746, A006749, A006748.

Formula

a(n)=A144553(n) + A056877(n) + 2 * A006747(n) + 2 * A006746(n) + 4 * A006749(n) + A006748(n).