A159866 Number of 2-sided n-polycairos.

1, 2, 5, 17, 55, 206, 781, 3099, 12421, 50725, 208870, 868238, 3631673, 15281827, 64610493

Offset

1,2

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 (from A121193)

I have counted the heptacairos in Brendan Owen's drawing. All 781=a(7) are there. - George Sicherman, Dec 06 2013

References

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

Links

Table of n, a(n) for n=1..15.

Ed Pegg, Jr., Illustrations of polyforms

Eric Weisstein's World of Mathematics, Polycairo

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 looks like a typo but I have not verified if the figure actually shows 781. - Joseph Myers, Oct 03 2011]

Livio Zucca, PolyMultiForms

Crossrefs

Cf. A151534, A151535, A151536.

Sequence in context: A149985 A149986 A121193 * A042671 A180148 A241133

Adjacent sequences: A159863 A159864 A159865 * A159867 A159868 A159869

Keyword

nonn,hard,more

Author

Eric W. Weisstein, Apr 24 2009

Extensions

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

Status

approved