A304076 - OEIS

%I #16 May 16 2018 13:20:47

%S 1,2,4,8,16,24,39,44,61,72,98,88,110,100,136,136,187,188,234,184,211,

%T 156,208,204,279,272,337,292,358,292,374,332,440,432,523,388,425,268,

%U 352,340,463,440,537,480,586,472,586,484,636,616,775,632,730,508,619

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

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

%C      +-----+

%C      |     |

%C      |  +--+

%C      |  |  |

%C      +--+  +--+--+

%C      |  |     |  |

%C      |  O--+--+  +

%C      |     |     |

%C      +-----+-----+

%C 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.

%C See A304077 for a variant of this sequence.

%C See A304050 for a similar sequence.

%H Rémy Sigrist, <a href="/A304076/b304076.txt">Table of n, a(n) for n = 0..515</a>

%H Rémy Sigrist, <a href="/A304076/a304076.png">Illustration of first terms</a>

%H Rémy Sigrist, <a href="/A304076/a304076.txt">C++ program for A304076</a>

%H Tilings Encyclopedia, <a href="https://tilings.math.uni-bielefeld.de/substitution/chair/">Chair</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aperiodic_tiling#Substitutions">Substitutions</a>

%H <a href="/index/Con#coordination_sequences">Index entries for coordination sequences of aperiodic tilings</a>

%o (C++) See Links section.

%Y Cf. A304050, A304077, A304078 (partial sums).

%K nonn

%O 0,2

%A _Rémy Sigrist_, May 06 2018