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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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11
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) = 1 - A035263(n-1). - Reinhard Zumkeller, Aug 16 2006
Comments from Paolo P. Lava , 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
| 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
| Recurrence: a(2*n) = 0, a(4*n+1) = 1, a(4*n+3) = a(n). [Ralf Stephan, Dec 11 2004]
Dirichlet g.f.: zeta(s)/(1+2^s). [Ralf Stephan, Jun 17 2007]
Let T(x) be the g.f., then T(x)+T(x^2)=x^2/(1-x^2). [Joerg Arndt, May 11 2010]
Let 2^k||n+1. Then a(n)=1 if k is odd, a(n)=0 if k is even. [Vladimir Shevelev, Aug 25 2010]
A096268(n) == A007814(n)(mod 2). - Robert G. Wilson v, Jan 18 2012
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EXAMPLE
| Start: 0
Rules:
0 --> 01
1 --> 00
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0: (#=1)
0
1: (#=2)
01
2: (#=4)
0100
3: (#=8)
01000101
4: (#=16)
0100010101000100
5: (#=32)
01000101010001000100010101000101
6: (#=64)
0100010101000100010001010100010101000101010001000100010101000100
7: (#=128)
010001010100010001000101010001010100010101000100010001010100010001000101010...
[Joerg Arndt, Jul 06 2011]
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MATHEMATICA
| Nest[ Flatten[ # /. {0 -> {1, 0}, 1 -> {0, 0}}] &, {1}, 7] (from Robert G. Wilson v Mar 05 2005)
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CROSSREFS
| Not the same as A073059! Cf. A096269, A096270, A071858, A096271.
Sequence in context: A110161 A134667 A117943 * A079101 A076478 A091444
Adjacent sequences: A096265 A096266 A096267 * A096269 A096270 A096271
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2004
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EXTENSIONS
| 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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