%I A029883
%S A029883 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,
%T A029883 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,
%U A029883 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
%V A029883 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,
%W A029883 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,
%X A029883 -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
%N A029883 First differences of Thue-Morse sequence A001285.
%C A029883 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
%H A029883 J.-P. Allouche and J. O. Shallit, <a href="http://www.cs.uwaterloo.ca/
               ~shallit/Papers/ubiq.ps">The Ubiquitous Prouhet-Thue-Morse Sequence</
               a>, in C. Ding. T. Helleseth and H. Niederreiter, eds., Sequences 
               and Their Applications: Proceedings of SETA '98, Springer-Verlag, 
               1999, pp. 1-16.
%F A029883 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.
%F A029883 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
%F A029883 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
%t A029883 Nest[ Function[ l, {Flatten[(l /. {0 -> {1, -1}, 1 -> {1, 0, -1}, -1 
               -> {0}})]}], {1}, 7] (from Robert G. Wilson v Feb 26 2005)
%o A029883 (PARI) a(n)=if(n<1|valuation(n,2)%2,0,-(-1)^subst(Pol(binary(n)),x,1)) 
               /* Michael Somos Jul 08 2004 */
%Y A029883 Apart from signs, same as A035263. Cf. A001285, A036554, A091785, A091855.
%Y A029883 a(n+1) = A036577(n) - 1 = A036585(n) - 2.
%Y A029883 Sequence in context: A078616 A104106 A141260 this_sequence A035263 A089045 
               A070749
%Y A029883 Adjacent sequences: A029880 A029881 A029882 this_sequence A029884 A029885 
               A029886
%K A029883 sign
%O A029883 1,1
%A A029883 N. J. A. Sloane (njas(AT)research.att.com).
%E A029883 Edited by Ralf Stephan, Dec 09 2004