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A005713
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Define strings S(0)=0, S(1)=11, S(n) = S(n-1)S(n-2); iterate.
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3
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1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(A035336(n)) = 0. [Reinhard Zumkeller, Dec 30 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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FORMULA
| For n>1, a(n-1)=floor(phi*ceiling(n/phi))-ceiling(phi*floor(n/phi)) where phi=(1+sqrt(5))/2. For n>=0, a(n)=abs(A005713(n+1)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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EXAMPLE
| The infinite word is S(infinity) = 110111101101111011110110...
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PROG
| (PARI) a(n, f1, f2)=local(f3); for(i=3, n, f3=concat(f2, f1); f1=f2; f2=f3); f2
(PARI) printp(a(10, [ 0 ], [ 1, 1 ])) \\ Would give S(10). Sequence is S(infinity).
(Haskell)
a005713 n = a005713_list !! n
a005713_list = 1 : 1 : concat (sibb [0] [1, 1]) where
sibb xs ys = zs : sibb ys zs where zs = xs ++ ys
-- Reinhard Zumkeller, Dec 30 2011
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CROSSREFS
| Cf. A005614, A003849.
Sequence in context: A118828 A105234 A181183 * A085241 A105368 A138019
Adjacent sequences: A005710 A005711 A005712 * A005714 A005715 A005716
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected by Michael Somos
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