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Search: id:A029883
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| 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, 1, -1, 0, 1, 0, -1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Fixed point of the morphism a->abc, b->ac, c->b, with a = 1, b = 0, c = -1, starting with a(1) = 1. - DELEHAM Philippe
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LINKS
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J.-P. Allouche and J. O. Shallit, The Ubiquitous Prouhet-Thue-Morse Sequence, in C. Ding. T. Helleseth and H. Niederreiter, eds., Sequences and Their Applications: Proceedings of SETA '98, Springer-Verlag, 1999, pp. 1-16.
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FORMULA
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Recurrence: a(4n) = a(n), a(4n+1) = a(2n+1), a(4n+2) = 0, a(4n+3) = -a(2n+1), starting a(1) = 1.
a(n) = 2 - A007413(n) . a(A036554(n)) = 0; a(A091785(n)) = -1; a(A091855(n)) = 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 20 2004
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v+w+u^2-v^2+2w^2-2uw. - Michael Somos Jul 08 2004
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MATHEMATICA
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Nest[ Function[ l, {Flatten[(l /. {0 -> {1, -1}, 1 -> {1, 0, -1}, -1 -> {0}})]}], {1}, 7] (from Robert G. Wilson v Feb 26 2005)
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PROGRAM
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(PARI) a(n)=if(n<1|valuation(n, 2)%2, 0, -(-1)^subst(Pol(binary(n)), x, 1)) /* Michael Somos Jul 08 2004 */
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CROSSREFS
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Apart from signs, same as A035263. Cf. A001285, A036554, A091785, A091855.
a(n+1) = A036577(n) - 1 = A036585(n) - 2.
Sequence in context: A078616 A104106 A141260 this_sequence A035263 A089045 A070749
Adjacent sequences: A029880 A029881 A029882 this_sequence A029884 A029885 A029886
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Ralf Stephan, Dec 09 2004
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