A342538 Number of free polyominoes with n cells having simply-connected interiors such that no smaller polyomino has the same bracelet.

1, 0, 1, 2, 4, 7, 17, 40, 101, 259, 671, 1741, 4689, 12511, 33603, 91249

Offset: 1

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Keywords

• nonn
• more

Comments

Consider only the corners of the polygon that forms the border of the polyomino. Then build the bracelet of black and white beads by following the border of the polygon in a clockwise direction, adding a black bead for each right-turning right angle, and a white bead for each left-turning right angle. Count in this sequence only polyominoes for which no smaller polyomino has the same bracelet. Note 2 polyominoes of the same size having the same bracelet will count as 2.

Examples

			a(2) is 0 as the domino has bracelet BBBB, which is the same as the monomino.
		

Crossrefs

Cf. A342537.