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A197465
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Number of free tetrakis polyaboloes (poly-[4.8^2]-tiles) with n cells, allowing holes, where division into tetrakis cells (triangular quarters of square grid cells) is significant.
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14
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1, 2, 2, 6, 8, 22, 42, 112, 252, 650, 1584, 4091, 10369, 26938, 69651, 182116, 476272, 1253067, 3302187, 8733551, 23142116, 61477564, 163612714, 436278921, 1165218495, 3117021788
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OFFSET
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1,2
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COMMENTS
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See the link below for a definition of the tetrakis square tiling. When a square grid cell is divided into triangles, it must be divided dexter (\) or sinister (/) according to the parity of the grid cell.
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REFERENCES
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Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.
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LINKS
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EXAMPLE
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For n=3 there are 4 triaboloes. Of these, 2 conform to the tetrakis grid. Each of these 2 has a unique dissection into 6 tetrakis cells. - George Sicherman, Mar 25 2021
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CROSSREFS
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Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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