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Search: id:A105969
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| A105969 |
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Fixed point of the morphism 1 -> 123, 2 -> 212, 3 -> 345, 4 -> 434, 5 -> 561, 6 -> 656, starting from a(0) = 1. |
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+0
2
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| 1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 1, 4, 3, 4, 3, 4, 5, 4, 3, 4, 5, 6, 1, 6, 5, 6, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 2, 1, 2, 1, 2, 3
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Six-symbol substitution modeled on a hexagon loop.
Characteristic Polynomial: x^6-9*x^5+30*x^4-46*x^3+36*x^2-21*x+9=0 L-system shown as: bb = a /. 1 -> {1, 0} /. 2 -> {0.5, 0.8660254037844386} /. 3 -> {-0.5,0.8660254037844386} /. 4 -> {-1, 0} /. 5 -> {-0.5, -0.8660254037844386} /. 6 -> {0.5, -0.8660254037844386}; ListPlot[FoldList[Plus, {0, 0}, bb], PlotRange -> All, PlotJoined -> True, Axes -> False];
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MATHEMATICA
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Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 3}, 2 -> {2, 1, 2}, 3 -> {3, 4, 5}, 4 -> {4, 3, 4}, 5 -> {5, 6, 1}, 6 -> {6, 5, 6}} &], {1}, 5]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2005)
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CROSSREFS
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Sequence in context: A118121 A006968 A058207 this_sequence A163530 A114409 A049063
Adjacent sequences: A105966 A105967 A105968 this_sequence A105970 A105971 A105972
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 28 2005
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EXTENSIONS
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Edited and corrected by Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2005
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