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 A039963 The period-doubling sequence A035263 repeated. 11

%I

%S 1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,

%T 0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,

%U 1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1

%N The period-doubling sequence A035263 repeated.

%C An example of a d-perfect sequence.

%C Motzkin numbers mod 2. - _Benoit Cloitre_, Mar 23 2004

%C Let {a, b, c, c, a, b, a, b, a, b, c, c, a, b, ...} be the fixed point of the morphism: a -> ab, b -> cc, c -> ab, starting from a; then the sequence is obtained by taking a = 1, b = 1, c = 0. - _Philippe Deléham_, Mar 28 2004

%H Seiichi Manyama, <a href="/A039963/b039963.txt">Table of n, a(n) for n = 0..10000</a>

%H D. Kohel, S. Ling and C. Xing, <a href="http://www.maths.usyd.edu.au/u/kohel/doc/perfect.ps">Explicit Sequence Expansions</a>, in Sequences and their Applications, C. Ding, T. Helleseth, and H. Niederreiter, eds., Proceedings of SETA'98 (Singapore, 1998), 308-317, 1999.

%H E. Rowland, R. Yassawi, <a href="http://arxiv.org/abs/1310.8635">Automatic congruences for diagonals of rational functions</a>, arXiv preprint arXiv:1310.8635 [math.NT], 2013.

%F a(n) = A035263(1+floor(n/2)). - _Benoit Cloitre_, Mar 23 2004

%F a(n) = A040039(n) mod 2 = A002212(n+1) mod 2. a(0) = a(1) = 1, for n>=2: a(n) = ( a(n) + Sum_{k=0..n-2} a(k)*a(n-2-k)) mod 2. - _Philippe Deléham_, Mar 26 2004

%F a(n) = (A(n+2) - A(n)) mod 2, for A = A019300, A001285, A010060, A010059, A000069, A001969. - _Philippe Deléham_, Mar 28 2004

%F a(n) = A001006(n) mod 2 = A092444(n). - _Christian G. Bower_, Jun 12 2005

%F a(n) = (-1)^n*(A096268(n+1) - A096268(n)). - _Johannes W. Meijer_, Feb 02 2013

%t Flatten[ Nest[ Function[l, {Flatten[(l /. {a -> {a, b}, b -> {c, c}, c -> {a, b}})]}], {a}, 7] /. {a -> {1}, b -> {1}, c -> {0}}] (* _Robert G. Wilson v_, Feb 26 2005 *)

%Y Cf. A081706.

%Y Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Christian G. Bower_, Jun 12 2005

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew Plewe_ and _Ralf Stephan_, Jul 13 2007

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Last modified May 27 13:57 EDT 2018. Contains 304694 sequences. (Running on oeis4.)