

A303981


Coordination sequence for a node with global 8fold symmetry in the AmmannBeenker tiling (also known as the Standard Octagonal tiling).


2



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
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OFFSET

0,2


COMMENTS

Although there are infinitely many inequivalent vertices with local eightfold symmetry in the tiling, there is (presumably) a unique vertex with global eightfold symmetry, which makes this sequence welldefined.  N. J. A. Sloane, Oct 20 2018


REFERENCES

F. P. M. Beenker, Algebraic theory of nonperiodic tilings of the plane by two simple building blocks: a square and a rhombus, Eindhoven University of Technology 1982, THReport, 82WSK04.
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

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, AmmannBeenker
Wikipedia, AmmannBeenker tiling
Index entries for coordination sequences of aperiodic tilings


PROG

(C++) See Links section.


CROSSREFS

Cf. A302841, A302842, A304033 (partial sums).
Sequence in context: A266086 A018922 A290287 * A285315 A020948 A219547
Adjacent sequences: A303978 A303979 A303980 * A303982 A303983 A303984


KEYWORD

nonn,changed


AUTHOR

Rémy Sigrist, May 04 2018


STATUS

approved



