This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159866 Number of 2-sided n-polycairos. 5
1, 2, 5, 17, 55, 206, 781, 3099, 12421, 50725, 208870, 868238, 3631673, 15281827, 64610493 (list; graph; refs; listen; history; text; internal format)



Consider the Laves tiling of the plane by equilateral pentagons with two 90-degree angles (and all edges equal), with symbol [3^], 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


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


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


Cf. A151534, A151535, A151536.

Sequence in context: A149985 A149986 A121193 * A042671 A180148 A241133

Adjacent sequences:  A159863 A159864 A159865 * A159867 A159868 A159869




Eric W. Weisstein, Apr 24 2009


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 16:42 EST 2019. Contains 329879 sequences. (Running on oeis4.)