A159866 Number of 2-sided n-polycairos.

1, 2, 5, 17, 55, 206, 781, 3099, 12421, 50725, 208870, 868238, 3631673, 15281827, 64610493, 274346429, 1169219224, 4999544053, 21440702381, 92192889106

Offset: 1

Author

Eric W. Weisstein, Apr 24 2009

Keywords

• nonn
• hard
• more

Comments

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

References

• Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.

Links

• Brendan Owen, The 17 tetra-Cairos (from the Zucca web site).
• Brendan Owen, The 55 penta-Cairos (from the Zucca web site).
• Brendan Owen, The 206 hexa-Cairos (from the Zucca web site).
• Brendan Owen, The 781 hepta-Cairos (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]
• Ed Pegg, Jr., Illustrations of polyforms
• Eric Weisstein's World of Mathematics, Polycairo
• Livio Zucca, PolyMultiForms

Crossrefs

Cf. A151534, A151535, A151536.

Extensions

a(11)-a(15) from Joseph Myers, Oct 03 2011

a(16)-a(20) from Bert Dobbelaere, Jun 02 2025