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Search: id:A096268
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| A096268 |
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Period-doubling sequence: fixed point of the morphism 0 -> 01, 1 -> 00. |
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+0
8
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| 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = 1 - A035263(n-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 16 2006
Comments from Paolo P. Lava (ppl(AT)spl.at), Apr 14 2008: (Start) At the m-th step (m=0,1,2,3,..., starting with 0 at step m=0) form the concatenation of the partial sequence (of length 2^m) with itself changing only the last digit (1 -> 0, 0 ->1). Thus
m=0 -> 0
m=1 -> 0 U 1 -> 01
m=2 -> 01 U 00 -> 0100
m=3 -> 0100 U 0101 -> 01000101
m=4 -> 01000101 U 01000100 -> 0100010101000100
etc. (End)
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1022
J.-P. Allouche, M. Baake, J. Cassaigns and D. Damanik, Palindrome complexity
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FORMULA
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Recurrence: a(2n) = 0, a(4n+1) = 1, a(4n+3) = a(n). - Ralf Stephan, Dec 11 2004
Dirichlet g.f.: zeta(s)/(1+2^s). - Ralf Stephan, Jun 17 2007
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MATHEMATICA
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Nest[ Function[l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {0, 0}})]}], {0}, 7] (from Robert G. Wilson v Feb 26 2005)
Nest[ Flatten[ # /. {0 -> {1, 0}, 1 -> {0, 0}}] &, {1}, 7] (from Robert G. Wilson v Mar 05 2005)
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CROSSREFS
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Not the same as A073059! Cf. A096269, A096270, A071858, A096271.
Sequence in context: A110161 A134667 A117943 this_sequence A079101 A076478 A091444
Adjacent sequences: A096265 A096266 A096267 this_sequence A096269 A096270 A096271
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KEYWORD
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nonn
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AUTHOR
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njas, Jun 22 2004
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EXTENSIONS
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Corrected by Jeremy Gardiner, Dec 12 2004
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 26 2005
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