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A304050 Coordination sequence for one of the inner vertices introduced in the first inflation-deflation step in a Half-Hex tiling. 4
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 (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; 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 * A242394 A030568 A017593

Adjacent sequences:  A304047 A304048 A304049 * A304051 A304052 A304053

KEYWORD

nonn

AUTHOR

Rémy Sigrist, May 05 2018

STATUS

approved

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Last modified December 3 20:56 EST 2020. Contains 338920 sequences. (Running on oeis4.)