

A197459


Number of free poly[3.6.3.6]tiles (holes allowed) with n cells (division into rhombi is significant).


15



1, 1, 3, 4, 12, 27, 78, 208, 635, 1859, 5726, 17526, 54620, 170479, 536714, 1694567, 5376764, 17110286, 54631302, 174879997, 561229678, 1805022806
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OFFSET

1,3


COMMENTS

[3.6.3.6] refers to the face configuration of the rhombille tiling.  Peter Kagey, Mar 01 2020
If we draw the short diagonals of each tile in the rhombille tiling, we get a subset of edges of the regular hexagonal grid; two edges are adjacent if and only if the corresponding rhombi are adjacent. These are polyedges where angles are constrained to 120 degrees. So there is a 1to1 correspondence with the subset of polyedges counted in A159867 after removing polyedges with angles of 60 and/or 180 degrees.  Joseph Myers, Jul 12 2020
These are also known as polytwigs, by association with their representation as polyedges.  Aaron N. Siegel, May 15 2022


REFERENCES

Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.


LINKS



CROSSREFS

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).


KEYWORD

hard,nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



