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A029883 First differences of Thue-Morse sequence A001285. 9
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Fixed point of the morphism a->abc, b->ac, c->b, with a = 1, b = 0, c = -1, starting with a(1) = 1. - Philippe Deléham

LINKS

Table of n, a(n) for n=1..105.

J.-P. Allouche and Jeffrey 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.

T. W. Cusick, H. Fredricksen and P. Stănică, On the delta sequence of the Thue-Morse sequence, Australas. J. Combin. 39 (2007), 293--300. [From N. J. A. Sloane, Dec 11 2009]

FORMULA

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. - Philippe Deléham, 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

MATHEMATICA

Nest[ Function[ l, {Flatten[(l /. {0 -> {1, -1}, 1 -> {1, 0, -1}, -1 -> {0}})]}], {1}, 7] (* Robert G. Wilson v, Feb 26 2005 *)

PROG

(PARI) a(n)=if(n<1|valuation(n, 2)%2, 0, -(-1)^subst(Pol(binary(n)), x, 1)) /* Michael Somos, Jul 08 2004 */

(PARI) a(n)=hammingweight(n)%2-hammingweight(n-1)%2 \\ Charles R Greathouse IV, Mar 26 2013

CROSSREFS

Apart from signs, same as A035263. Cf. A001285, A036554, A091785, A091855.

a(n+1) = A036577(n) - 1 = A036585(n) - 2.

Sequence in context: A104106 A141260 * A035263 A089045 A070749 A059778

Adjacent sequences:  A029880 A029881 A029882 * A029884 A029885 A029886

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

EXTENSIONS

Edited by Ralf Stephan, Dec 09 2004

STATUS

approved

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Last modified November 26 19:08 EST 2014. Contains 250103 sequences.