A351142 Free chiral polyominoes with n squares, having 90-degree rotational symmetry about the center of a square of the underlying square matrix.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 3, 7, 0, 0, 14, 25, 0, 0, 55, 90, 0, 0, 216, 319, 0, 0, 816, 1136, 0, 0, 3098, 4088, 0, 0, 11711, 14868, 0, 0, 44462, 54526, 0, 0, 169213, 201527, 0, 0, 646441, 750169, 0, 0, 2477819, 2809931, 0, 0, 9530788, 10582370, 0, 0, 36768799, 40043785

Offset: 1

Author

John Mason, Feb 02 2022

Keywords

• nonn
• hard

Comments

The sequence enumerates a subset of the polyominoes enumerated by A144553.

Examples

			a(12)=1 because of:
   O
   OOOO
   O O
  OOOO
     O
		

Crossrefs

Cf. A000105, A144553, A234007.

Formula

For n multiple of 4, a(n) = A144553(n) - A234007(n/4); otherwise a(n) = A144553(n).