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A349197
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a(n) is the X-coordinate of the n-th point of the alternate terdragon curve; sequence A349198 gives Y-coordinates.
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3
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0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 6, 6, 7, 7, 6, 6, 5, 5, 6, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7, 8, 7, 7, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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COMMENTS
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Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):
Y
/
/
0 ---- X
The alternate terdragon curve can be represented using an L-system.
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LINKS
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Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, 2011, pages 571-614. See end of section 5.
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FORMULA
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a(9^k) = 3^k for any k >= 0.
a(9*n) = 3*a(n).
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EXAMPLE
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The alternate terdragon curve starts as follows:
14
\
\
2----3,12--10,13
\ / \ / \
\ / \ / \
0----1,4--5,8,11--9
/ \
/ \
6-----7
- so a(0) = a(2) = 0,
a(1) = a(3) = a(4) = a(12) = a(14) = 1.
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A349040 for a similar sequence.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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