

A159866


Number of 2sided npolycairos.


5



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

1,2


COMMENTS

Consider the Laves tiling of the plane by equilateral pentagons with two 90degree 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 ncelled 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 tetraCairos (from the Zucca web site).
Brendan Owen, The 55 pentaCairos (from the Zucca web site).
Brendan Owen, The 206 hexaCairos (from the Zucca web site).
Brendan Owen, The 781 heptaCairos (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



