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A156595
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Fixed point of the morphism 0->011, 1->010.
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4
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0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This sequence draws the Sierpinski gasket, when iterating the following odd-even drawing rule : If "1" then draw a segment forward, if "0" then draw a segment forward and turn 120A degs right if in odd position or left if in even position.
Contribution from Dimitri Hendriks (diem(AT)cs.vu.nl), Jun 29 2010: (Start)
This sequence is the first difference of the Mephisto Waltz A064990, i.e., a(n) = A064990(n) + A064990(n+1), where `+' is addition modulo 2.
This sequence can also be generated as a Toeplitz word: First consider the periodic word 0,1,$,0,1,$,0,1,$,... and then fill the gaps $ by the bitwise negation of the sequence itself: 0,1,_1_,0,1,_0_,0,1,_0_,.... See [1] for a precise definition of Toeplitz sequences.
[1] Allouche & Bacher, Toeplitz Sequences, Paperfolding, Towers of Hanoi, and Progression-Free Sequences of Integers. In: L'Enseignement Math'ematique, volume 38, pages 315-327, 1992. (End)
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REFERENCES
| Combinatoris on words, M Lothaire.
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FORMULA
| apply morphism iteratively to infinity : 0->011 and 1->010.
a(3k-2)=0, a(3k-1)=1, a(3k)=1-a(k) for k>=1, a(0)=0. [From Clark Kimberling, Apr 28 2011]
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EXAMPLE
| 0 -> 0,1,1 -> 0,1,1,0,1,0,0,1,0 -> ...
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MATHEMATICA
| Nest[ Flatten[ # /. {0 -> {0, 1, 1}, 1 -> {0, 1, 0}}] &, {0}, 10]
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CROSSREFS
| Cf. A189628.
Sequence in context: A057215 A029691 A053866 * A143222 A010060 A118247
Adjacent sequences: A156592 A156593 A156594 * A156596 A156597 A156598
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Feb 10 2009
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EXTENSIONS
| Corrected two typos. - Dimitri Hendriks (diem(AT)cs.vu.nl), Jun 29 2010
Added: "where `+' is addition modulo 2" to the first sentence of first comment Dimitri Hendriks (diem(AT)cs.vu.nl), Jul 18 2010
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