Search: id:A096268
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%I A096268
%S A096268 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,
%T A096268 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,
%U A096268 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
%N A096268 Period-doubling sequence: fixed point of the morphism 0 -> 01, 1 -> 00.
%C A096268 a(n) = 1 - A035263(n-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 16 2006
%C A096268 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
%C A096268 m=0 -> 0
%C A096268 m=1 -> 0 U 1 -> 01
%C A096268 m=2 -> 01 U 00 -> 0100
%C A096268 m=3 -> 0100 U 0101 -> 01000101
%C A096268 m=4 -> 01000101 U 01000100 -> 0100010101000100
%C A096268 etc. (End)
%H A096268 T. D. Noe, <a href="b096268.txt">Table of n, a(n) for n=0..1022</a>
%H A096268 J.-P. Allouche, M. Baake, J. Cassaigns and D. Damanik, <a href="http:/
               /www.lri.fr/~allouche/">Palindrome complexity</a>
%F A096268 Recurrence: a(2n) = 0, a(4n+1) = 1, a(4n+3) = a(n). - Ralf Stephan, Dec 
               11 2004
%F A096268 Dirichlet g.f.: zeta(s)/(1+2^s). - Ralf Stephan, Jun 17 2007
%t A096268 Nest[ Function[l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {0, 0}})]}], {0}, 
               7] (from Robert G. Wilson v Feb 26 2005)
%t A096268 Nest[ Flatten[ # /. {0 -> {1, 0}, 1 -> {0, 0}}] &, {1}, 7] (from Robert 
               G. Wilson v Mar 05 2005)
%Y A096268 Not the same as A073059! Cf. A096269, A096270, A071858, A096271.
%Y A096268 Sequence in context: A110161 A134667 A117943 this_sequence A079101 A076478 
               A091444
%Y A096268 Adjacent sequences: A096265 A096266 A096267 this_sequence A096269 A096270 
               A096271
%K A096268 nonn
%O A096268 0,1
%A A096268 N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2004
%E A096268 Corrected by Jeremy Gardiner, Dec 12 2004
%E A096268 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 26 2005

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