cp's OEIS Frontend

A159866 Number of 2-sided n-polycairos.

%I A159866 #35 Jun 02 2025 12:19:58
%S A159866 1,2,5,17,55,206,781,3099,12421,50725,208870,868238,3631673,15281827,
%T A159866 64610493,274346429,1169219224,4999544053,21440702381,92192889106
%N A159866 Number of 2-sided n-polycairos.
%C A159866 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
%D A159866 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.
%H A159866 Brendan Owen, <a href="/A121193/a121193_4.gif">The 17 tetra-Cairos</a> (from the Zucca web site).
%H A159866 Brendan Owen, <a href="/A121193/a121193_5.gif">The 55 penta-Cairos</a> (from the Zucca web site).
%H A159866 Brendan Owen, <a href="/A121193/a121193_6.gif">The 206 hexa-Cairos</a> (from the Zucca web site).
%H A159866 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 is a typo: the figure actually shows a(7)=781 heptacairos. - _Joseph Myers_, Oct 03 2011, and _George Sicherman_, Dec 06 2013]
%H A159866 Ed Pegg, Jr., <a href="http://demonstrations.wolfram.com/PolyformExplorer/">Illustrations of polyforms</a>
%H A159866 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polycairo.html">Polycairo</a>
%H A159866 Livio Zucca, <a href="http://www.iread.it/lz/polymultiforms2.html">PolyMultiForms</a>
%Y A159866 Cf. A151534, A151535, A151536.
%K A159866 nonn,hard,more
%O A159866 1,2
%A A159866 _Eric W. Weisstein_, Apr 24 2009
%E A159866 a(11)-a(15) from _Joseph Myers_, Oct 03 2011
%E A159866 a(16)-a(20) from _Bert Dobbelaere_, Jun 02 2025