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A197459 Number of free poly-[]-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 (list; graph; refs; listen; history; text; internal format)



[] 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 1-to-1 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


Branko Gr├╝nbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.


Table of n, a(n) for n=1..17.

Peter Kagey, Illustration for A197459(4) = 4.

R. J. Mathar, OEIS A197459

Wikipedia, Rhombille tiling


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




Joseph Myers, Oct 15 2011



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Last modified September 21 09:06 EDT 2021. Contains 347597 sequences. (Running on oeis4.)