

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
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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


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

Table of n, a(n) for n=1..17.
Peter Kagey, Illustration for A197459(4) = 4.
R. J. Mathar, OEIS A197459
Wikipedia, Rhombille tiling


CROSSREFS

Cf. A197460, A197461.
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).
Sequence in context: A343163 A000942 A255436 * A330659 A000207 A002986
Adjacent sequences: A197456 A197457 A197458 * A197460 A197461 A197462


KEYWORD

hard,nonn,more


AUTHOR

Joseph Myers, Oct 15 2011


STATUS

approved



