%I
%S 1,1,2,5,15,54,212,908,4011,18260,84320
%N Number of diagonal polyominoes with n cells.
%C Apparently the cells are circular blobs which must be connected diagonally and the polyominoes can be rotated by 90 degrees and turned over.
%C 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
%H R. J. Mathar, <a href="/A056841/a056841.gz">Table of all such polyominoes with n <= 10 cells</a> (gzipped)
%H R. J. Mathar, <a href="/A056841/a056841.cpp.txt">C++ program</a>
%H Douglas A. Torrance, <a href="https://arxiv.org/abs/1906.01541">Enumeration of planar Tangles</a>, arXiv:1906.01541 [math.CO], 20192020. See Table 4.1 (C).
%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/minio/images/d1.gif">The 15 5celled diagonal polyominoes</a>
%H M. Vicher, <a href="/A056841/a056841.gif">The 15 5celled diagonal polyominoes</a>
%e The polyominoes with 1, 2, 3 and 4 cells are
%e O..O...O...O.O..O....O....O.....O....O.O
%e ....O...O...O....O....O....O...O.O..O.O.
%e .........O........O....O..O.O...O.......
%e ...................O..O.................
%Y See also A056840, A056787.
%K nonn,nice,more
%O 1,3
%A _James A. Sellers_, Aug 28 2000
%E Description revised by _N. J. A. Sloane_, Jun 21 2001
%E a(10) from _R. J. Mathar_, Apr 10 2006
%E a(11) from _Douglas A. Torrance_, Mar 06 2020
