A056786 Number of inequivalent connected planar figures that can be formed from n non-overlapping 1 X 2 rectangles (or dominoes).

1, 1, 4, 26, 255, 2874, 35520, 454491, 5954914, 79238402, 1067193518

Offset: 0

Author

James Sellers, Aug 28 2000

Keywords

• nonn
• nice
• more

Comments

"Connected" means "connected by edges", rotations and reflections are not considered different, but the internal arrangement of the dominoes does matter.

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.

Links

• Gordon Hamilton, Three integer sequences from recreational mathematics, Video (2013?).
• R. J. Mathar, Illustration of the 255 figures for the 4th term
• N. J. A. Sloane, Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581
• N. J. A. Sloane, Illustration of third term of A056786, A216598, A216583, A216595, A216492, A216581 (a better drawing for the third term)
• M. Vicher, Polyforms
• Index entries for sequences related to dominoes

Crossrefs

Cf. A121194, A216598, A216583, A216595, A216492, A216581.

Extensions

Edited by N. J. A. Sloane, Aug 17 2006, May 15 2010, Sep 09 2012

a(6) and a(7) from Owen Whitby, Nov 18 2009

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.

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).

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!]