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A159866
Number of 2-sided n-polycairos.
5
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
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
KEYWORD
nonn,hard,more
AUTHOR
Eric W. Weisstein, Apr 24 2009
EXTENSIONS
a(11)-a(15) from Joseph Myers, Oct 03 2011
STATUS
approved