A304077 - OEIS

%I #16 Jan 08 2019 03:02:32

%S 1,4,12,24,36,52,52,72,92,120,84,104,116,168,156,204,220,260,148,168,

%T 164,248,244,308,300,368,284,344,300,408,364,472,500,564,276,296,260,

%U 408,420,516,460,560,500,608,444,568,524,704,708,844,556,612,460,632

%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; this vertex is tetravalent from the second inflation-deflation step onwards):

%C      +-----+

%C      |     |

%C      |  +--+

%C      |  |  |

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

%C      |  |     |  |

%C      |  +--+--+  +

%C      |     |     |

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

%C After k > 1 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 1 < i < j, c_i is a prefix of c_j; this sequence is the limiting sequence of the { c_i, i > 1 } family.

%C See A304076 for a variant of this sequence.

%C See A304050 for a similar sequence.

%H Rémy Sigrist, <a href="/A304077/b304077.txt">Table of n, a(n) for n = 0..512</a>

%H Rémy Sigrist, <a href="/A304077/a304077.png">Illustration of first terms</a>

%H Rémy Sigrist, <a href="/A304077/a304077.txt">C++ program for A304077</a>

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

%H <a href="/index/Con#coordination_sequences">Index entries for sequences related to coordination sequences</a>

%o (C++) See Links section.

%Y Cf. A304050, A304076, A304079 (partial sums).

%K nonn

%O 0,2

%A _Rémy Sigrist_, May 06 2018