A304077 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, 4, 12, 24, 36, 52, 52, 72, 92, 120, 84, 104, 116, 168, 156, 204, 220, 260, 148, 168, 164, 248, 244, 308, 300, 368, 284, 344, 300, 408, 364, 472, 500, 564, 276, 296, 260, 408, 420, 516, 460, 560, 500, 608, 444, 568, 524, 704, 708, 844, 556, 612, 460, 632

Offset

0,2

Comments

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):

+-----+

| |

| +--+

| | |

+--O +--+--+

| | | |

| +--+--+ +

| | |

+-----+-----+

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.

See A304076 for a variant of this sequence.

See A304050 for a similar sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..512

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, C++ program for A304077

Tilings Encyclopedia, Chair

Index entries for sequences related to coordination sequences

Prog

(C++) See Links section.

Crossrefs

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

Sequence in context: A317518 A307763 A071228 * A108997 A159795 A301171

Adjacent sequences: A304074 A304075 A304076 * A304078 A304079 A304080

Keyword

nonn

Author

Rémy Sigrist, May 06 2018

Status

approved