A304910 Coordination sequence for the inner vertex introduced in the first inflation-deflation step in a Pinwheel tiling.

1, 8, 26, 38, 44, 68, 92, 100, 138, 122, 182, 192, 198, 224, 204, 236, 256, 276, 272, 276, 328, 372, 384, 396, 352, 436, 496, 428, 510, 490, 500, 552, 572, 580, 602, 662, 666, 672, 678, 704, 692, 724, 744, 656, 704, 908, 880, 892, 984, 794, 1014, 944, 812

Offset

0,2

Comments

The first inflation-deflation step leads to the following configuration (where O marks the reference vertex for this sequence):

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|||||||||--\\

||||||||----\\\\

|||||||------\\\\\\

|||||||-------\\\\\\\\

||||||---------\\\\\\\\\\

|||||O----------\\\\\\\\\\\\

||||////---------\\\\\\\\\\....

||||///////--------\\\\\\\........

|||///////////------\\\\\............

||///////////////----\\\\...............

|///////////////////--\\...................

|//////////////////////.......................

After k > 0 inflation-deflation steps, we can compute a finite coordination sequence c_k (until we reach the edge of the tiling after k steps). It appears that for i and j such that 0 < i < j, c_i is a prefix of c_j; this sequence is the limiting sequence of the { c_i, i > 0 } family.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..902

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, PARI program for A304910

Tilings Encyclopedia, Pinwheel

Wikipedia, Pinwheel tiling

Index entries for coordination sequences of aperiodic tilings

Prog

(PARI) See Links section.

Crossrefs

Cf. A304913 (partial sums).

Sequence in context: A063560 A265104 A328205 * A271989 A069952 A031085

Adjacent sequences: A304907 A304908 A304909 * A304911 A304912 A304913

Keyword

nonn

Author

Rémy Sigrist, May 20 2018

Status

approved