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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 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 Table of n, a(n) for n=1..22. Abaroth's World, Illustration of a(1) through a(6) Peter Kagey, Illustration for A197459(4) = 4. R. J. Mathar, OEIS A197459 Wikipedia, Rhombille tiling CROSSREFS Cf. A019988, A159867, 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 EXTENSIONS a(18)-a(22) from Aaron N. Siegel, May 15 2022 STATUS approved

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Last modified August 5 10:59 EDT 2024. Contains 374950 sequences. (Running on oeis4.)