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Search: id:A020985
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| A020985 |
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The Golay-Rudin-Shapiro sequence. |
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+0
6
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| 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 78.
J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.
A. Hof, O. Knill and B. Simon, Singular continuous spectrum for palindromic Schroedinger operators, Commun. Math. Phys. 174 (1995), 149-159.
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LINKS
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Joerg Arndt, Fxtbook
J.-P. Allouche and M. Mendes France, Automata and Automatic Sequences.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a_0=1, a_2n = a_n, a_2n+1 = (-1)^n *a_n.
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MAPLE
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A020985 := proc(n) option remember; if n = 0 then 1 elif n mod 2 = 0 then A020985(n/2) else (-1)^((n-1)/2 )*A020985( (n-1)/2 ); fi; end;
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CROSSREFS
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Cf. A022155.
(-1)^A014081(n).
Sequence in context: A156734 A108784 A010555 this_sequence A034947 A097807 A014077
Adjacent sequences: A020982 A020983 A020984 this_sequence A020986 A020987 A020988
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KEYWORD
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sign,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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