A304050 Coordination sequence for one of the inner vertices introduced in the first inflation-deflation step in a Half-Hex tiling.

1, 6, 18, 30, 36, 48, 72, 78, 78, 96, 120, 138, 126, 132, 174, 180, 168, 186, 222, 240, 216, 222, 288, 282, 246, 276, 324, 348, 306, 306, 384, 384, 342, 366, 426, 450, 396, 396, 498, 486, 420, 456, 528, 570, 486, 468, 594, 588, 516, 546, 630, 660, 576, 570

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 hexavalent 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 and A304077 for similar sequences.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..1024

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, C++ program for A304050

Tilings Encyclopedia, Half-Hex

Index entries for coordination sequences of aperiodic tilings

Prog

(C++) See Links section.

Crossrefs

Cf. A304075 (partial sums), A304076, A304077.

Sequence in context: A225110 A077660 A240991 * A351220 A242394 A030568

Adjacent sequences: A304047 A304048 A304049 * A304051 A304052 A304053

Keyword

nonn

Author

Rémy Sigrist, May 05 2018

Status

approved