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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.
3

%I #10 Nov 06 2013 10:45:43

%S 1,2,10,84

%N 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.

%C 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.

%C 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.

%C See the Applegate link for further information.

%H David Applegate, <a href="/A121194/a121194.txt">Explanation of rules; examples; differences from A056755</a>

%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>

%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/new1/images/b1.gif">The 10 2-celled polyominoes mentioned in A056755</a>

%H M. Vicher, <a href="/A056755/a056755a.gif">The 10 2-celled polyominoes mentioned in A056755</a> [Taken from the Vicher web site]

%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/new1/images/p6.gif">The 68 3-celled polyominoes mentioned in A056755</a>

%H M. Vicher, <a href="/A056755/a056755b.gif">The 68 3-celled polyominoes mentioned in A056755</a> [Taken from the Vicher web site]

%Y Cf. A056755, A056786.

%K nice,nonn,more

%O 0,2

%A _David Applegate_