A304076 - OEIS

A304076

Coordination sequence for one of the inner vertices introduced in the first inflation-deflation step in a chair tiling (see Comments for precise definition).

1, 2, 4, 8, 16, 24, 39, 44, 61, 72, 98, 88, 110, 100, 136, 136, 187, 188, 234, 184, 211, 156, 208, 204, 279, 272, 337, 292, 358, 292, 374, 332, 440, 432, 523, 388, 425, 268, 352, 340, 463, 440, 537, 480, 586, 472, 586, 484, 636, 616, 775, 632, 730, 508, 619

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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

+-----+

| |

| +--+

| | |

+--+ +--+--+

| | | |

| 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.

See A304077 for a variant of this sequence.

See A304050 for a similar sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..515

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, C++ program for A304076

Tilings Encyclopedia, Chair

Wikipedia, Substitutions

Index entries for coordination sequences of aperiodic tilings

PROG

(C++) See Links section.

CROSSREFS