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A068599
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Number of n-uniform tilings.
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7
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11, 20, 61, 151, 332, 673, 1472, 2850, 5960, 11866, 24459, 49794, 103082
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OFFSET
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1,1
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COMMENTS
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Sequence gives the number of edge-to-edge regular-polygon tilings having n vertex classes relative to the symmetry of the tiling. Allows tilings with two or more vertex classes having the same arrangement of surrounding polygons (vertex type), as long as those classes are distinct within the symmetry of the tiling .
There are eleven 1-uniform tilings (also called the "Archimedean" tessellations) which comprise the three regular tessellations (all triangles, squares, or hexagons) plus the eight semiregular tessellations.
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REFERENCES
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Marek Čtrnáct, Postings to Tiling Mailing List, 2021 (a(13) announced in posting on Dec 21 2021).
B. Grünbaum and G. C. Shephard, Tilings and Patterns, an Introduction, Freeman, 1989; Exercise *6 on p. 70. See Sections 2.1 and 2.2.
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LINKS
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Brian Galebach, 7-Uniform Tiling Example, shows a tiling with 7 vertex classes (7-uniform), and 6 vertex types (6-Archimedean).
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)
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CROSSREFS
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KEYWORD
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hard,nice,more,nonn
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AUTHOR
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EXTENSIONS
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151 and 332 found by Brian Galebach on Apr 30 2002, 673 on Aug 06 2003, 1472 on Apr 28 2020
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STATUS
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approved
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