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A197465 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. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
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
EXAMPLE
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
CROSSREFS
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).
Sequence in context: A129383 A052957 A275441 * A074933 A157253 A003178
KEYWORD
nonn,hard,more
AUTHOR
Joseph Myers, Oct 15 2011
EXTENSIONS
Name clarified by George Sicherman, Mar 25 2021
a(21)-a(26) from Aaron N. Siegel, May 18 2022
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)