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

0,2

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

Table of n, a(n) for n=0..3.

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.

Sequence in context: A050390 A298690 A101878 * A302572 A121516 A024491

Adjacent sequences: A121191 A121192 A121193 * A121195 A121196 A121197

Keyword

nice,nonn,more

Author

David Applegate

Status

approved