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A303981
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Coordination sequence for a node with global 8-fold symmetry in the Ammann-Beenker tiling (also known as the Standard Octagonal tiling).
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2
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1, 8, 16, 32, 32, 40, 48, 72, 64, 96, 80, 104, 112, 112, 128, 152, 160, 144, 160, 168, 192, 216, 176, 208, 224, 232, 256, 240, 272, 264, 256, 296, 304, 336, 288, 312, 352, 320, 416, 312, 384, 392, 352, 432, 400, 456, 400, 416, 464, 440, 544, 416, 496, 488, 480
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Although there are infinitely many inequivalent vertices with local eight-fold symmetry in the tiling, there is (presumably) a unique vertex with global eight-fold symmetry, which makes this sequence well-defined. - N. J. A. Sloane, Oct 20 2018
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REFERENCES
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F. P. M. Beenker, Algebraic theory of non-periodic tilings of the plane by two simple building blocks: a square and a rhombus, Eindhoven University of Technology 1982, TH-Report, 82-WSK04.
A. Bellos and E. Harriss, Patterns of the Universe: A Coloring Adventure in Math and Beauty, unnumbered pages, 2015. See illustration about half-way through the book.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 0..985
Rémy Sigrist, Illustration of the first terms
M. Baake, U. Grimm, P. Repetowicz and D. Joseph, Coordination sequences and critical points. See for example Table 2.
Rémy Sigrist, C++ program for A303981
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)
Tilings Encyclopedia, Ammann-Beenker
Wikipedia, Ammann-Beenker tiling
Index entries for coordination sequences of aperiodic tilings
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PROG
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(C++) See Links section.
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CROSSREFS
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Cf. A302841, A302842, A304033 (partial sums).
Sequence in context: A266086 A018922 A290287 * A285315 A020948 A219547
Adjacent sequences: A303978 A303979 A303980 * A303982 A303983 A303984
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KEYWORD
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nonn,changed
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AUTHOR
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Rémy Sigrist, May 04 2018
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STATUS
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approved
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