

A056841


Number of diagonal polyominoes with n cells.


4



1, 1, 2, 5, 15, 54, 212, 908, 4011, 18260, 84320
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OFFSET

1,3


COMMENTS

Apparently the cells are circular blobs which must be connected diagonally and the polyominoes can be rotated by 90 degrees and turned over.
Also the number of essentially different (i.e. not related by reflections, translations or rotations) diagrams consisting of n nodes in Z^2 and n1 horizontal or vertical edges of length 1 between pairs of nodes such that the resulting graph is connected (hence a tree).  Paul Boddington, Jul 27 2004


LINKS

Table of n, a(n) for n=1..11.
R. J. Mathar, Table of all such polyominoes with n <= 10 cells (gzipped)
R. J. Mathar, C++ program
Douglas A. Torrance, Enumeration of planar Tangles, arXiv:1906.01541 [math.CO], 20192020. See Table 4.1 (C).
M. Vicher, Polyforms
M. Vicher, The 15 5celled diagonal polyominoes
M. Vicher, The 15 5celled diagonal polyominoes


EXAMPLE

The polyominoes with 1, 2, 3 and 4 cells are
O..O...O...O.O..O....O....O.....O....O.O
....O...O...O....O....O....O...O.O..O.O.
.........O........O....O..O.O...O.......
...................O..O.................


CROSSREFS

See also A056840, A056787.
Sequence in context: A006966 A336020 A277175 * A185040 A208237 A321958
Adjacent sequences: A056838 A056839 A056840 * A056842 A056843 A056844


KEYWORD

nonn,nice,more


AUTHOR

James A. Sellers, Aug 28 2000


EXTENSIONS

Description revised by N. J. A. Sloane, Jun 21 2001
a(10) from R. J. Mathar, Apr 10 2006
a(11) from Douglas A. Torrance, Mar 06 2020


STATUS

approved



