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%I #24 Nov 26 2015 04:19:24
%S 1,2,5,17,55,206,781,3099,12421,50725,208870,868238,3631673,15281827,
%T 64610493
%N Number of 2-sided n-polycairos.
%C Consider the Laves tiling of the plane by equilateral pentagons with two 90-degree angles (and all edges equal), with symbol [3^2.4.3.4], as seen for example in Fig. 2.7.1 of Grünbaum and Shephard, p. 96. Sequence gives number of n-celled connected animals that can be drawn on this grid. If we replace this tiling by the square grid tiling [4^4], we get the classical polyomino problem (see A000105). - _N. J. A. Sloane_, Aug 17 2006 (from A121193)
%C I have counted the heptacairos in Brendan Owen's drawing. All 781=a(7) are there. - _George Sicherman_, Dec 06 2013
%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.
%H Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polycairo.html">Polycairo</a>
%H Brendan Owen, <a href="/A121193/a121193_4.gif">The 17 tetra-Cairos</a> (from the Zucca web site).
%H Brendan Owen, <a href="/A121193/a121193_5.gif">The 55 penta-Cairos</a> (from the Zucca web site).
%H Brendan Owen, <a href="/A121193/a121193_6.gif">The 206 hexa-Cairos</a> (from the Zucca web site).
%H Brendan Owen, <a href="/A121193/a121193_7.gif">The 781 hepta-Cairos</a> (from the Zucca web site). [This site gives the number as 718, which looks like a typo but I have not verified if the figure actually shows 781. - Joseph Myers, Oct 03 2011]
%H Livio Zucca, <a href="http://www.iread.it/lz/polymultiforms2.html">PolyMultiForms</a>
%Y Cf. A151534, A151535, A151536.
%K nonn,hard,more
%O 1,2
%A _Eric W. Weisstein_, Apr 24 2009
%E a(11)-a(15) from _Joseph Myers_, Oct 03 2011
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