login
A303981
Coordination sequence for a node with global 8-fold symmetry in the Ammann-Beenker tiling (also known as the Standard Octagonal tiling).
3
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
OFFSET
0,2
COMMENTS
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
REFERENCES
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 halfway through the book.
LINKS
M. Baake, U. Grimm, P. Repetowicz and D. Joseph, Coordination sequences and critical points, arXiv:cond-mat/9809110 [cond-mat.stat-mech], 1998; in: S. Takeuchi and T. Fujiwara, Proceedings of the 6th International Conference on Quasicrystals - Yamada Conference XLVII, World Scientific Publishing, 1998, ISBN 981-02-3343-4, pp 124-127. See for example Table 2.
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
PROG
(C++) See Links section.
CROSSREFS
Cf. A302841, A302842, A304033 (partial sums).
Sequence in context: A266086 A018922 A290287 * A285315 A020948 A219547
KEYWORD
nonn
AUTHOR
Rémy Sigrist, May 04 2018
STATUS
approved