%I #49 May 18 2022 13:12:33
%S 1,1,4,26,255,2874,35520,454491,5954914,79238402,1067193518
%N Number of inequivalent connected planar figures that can be formed from n non-overlapping 1 X 2 rectangles (or dominoes).
%C "Connected" means "connected by edges", rotations and reflections are not considered different, but the internal arrangement of the dominoes does matter.
%C I have verified the first three entries by hand. The terms 255 and 2874 were taken from the Vicher web page. - _N. J. A. Sloane_.
%H Gordon Hamilton, <a href="http://youtu.be/7efCz2FvUDI">Three integer sequences from recreational mathematics</a>, Video (2013?).
%H R. J. Mathar, <a href="/A056786/a056786_1.pdf">Illustration of the 255 figures for the 4th term</a>
%H N. J. A. Sloane, <a href="/A056786/a056786.jpg">Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581</a>
%H N. J. A. Sloane, <a href="/A056786/a056786.pdf">Illustration of third term of A056786, A216598, A216583, A216595, A216492, A216581</a> (a better drawing for the third term)
%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%Y Cf. A121194, A216598, A216583, A216595, A216492, A216581.
%K nonn,nice,more
%O 0,3
%A _James A. Sellers_, Aug 28 2000
%E Edited by _N. J. A. Sloane_, Aug 17 2006, May 15 2010, Sep 09 2012
%E a(6) and a(7) from _Owen Whitby_, Nov 18 2009
%E a(8) from Anton Betten, Jan 18 2013, added by _N. J. A. Sloane_, Jan 18 2013. Anton Betten also verified that a(0)-a(7) are correct.
%E a(9) from Anton Betten, Jan 25 2013, added by _N. J. A. Sloane_, Jan 26 2013. Anton Betten comments that he used 8 processors, each for about 1 and a half day (roughly 300 hours CPU time).
%E a(10) from _Aaron N. Siegel_, May 18 2022. [It took just 30 minutes to verify a(9) and 7.2 hours to compute a(10), on a single CPU core!]