A121194 Number of n-celled polyominoes, where the cells are 1 X 2 rectangles with one edge of length 2 replaced by a curved arc that either sags inwards or bulges outwards, subject to some restrictions.

1, 2, 10, 84

Offset: 0

Author

David Applegate

Keywords

• nice
• nonn
• more

Comments

This is the result of trying to infer the rules behind A056755. The match is not exact - these rules allow 16 3-celled polyominoes not allowed in A056755. However, the reason for the exclusion of those 16 polyominoes in A056755 is not clear.

The restrictions are: all curved edges must be on the boundary of the polyomino, each side of the polyomino must be either all curved, or all straight and if two cells meet on a side of length 2, they must share the whole side. Polyominoes are allowed to be rotated and reflected.

See the Applegate link for further information.

Links

• David Applegate, Explanation of rules; examples; differences from A056755
• M. Vicher, Polyforms
• M. Vicher, The 10 2-celled polyominoes mentioned in A056755
• M. Vicher, The 10 2-celled polyominoes mentioned in A056755 [Taken from the Vicher web site]
• M. Vicher, The 68 3-celled polyominoes mentioned in A056755
• M. Vicher, The 68 3-celled polyominoes mentioned in A056755 [Taken from the Vicher web site]

Crossrefs

Cf. A056755, A056786.