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A039963
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The period-doubling sequence A035263 repeated.
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11
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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An example of a d-perfect sequence.
Motzkin numbers mod 2. - Benoit Cloitre, Mar 23 2004
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
The asymptotic mean of this sequence is 2/3 (Rowland and Yassawi, 2015; Burns, 2016). - Amiram Eldar, Jan 30 2021
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..10000
Rob Burns, Asymptotic density of Motzkin numbers modulo small primes, arXiv:1611.04910 [math.NT], 2016.
David Kohel, San Ling and Chaoping Xing, Explicit Sequence Expansions, in: C. Ding, T. Helleseth and H. Niederreiter (eds.), Sequences and their Applications, Proceedings of SETA'98 (Singapore, 1998), Discrete Mathematics and Theoretical Computer Science, 1999, pp. 308-317; alternative link.
Eric Rowland and Reem Yassawi, Automatic congruences for diagonals of rational functions, Journal de Théorie des Nombres de Bordeaux, Vol. 27, No. 1 (2015), pp. 245-288; arXiv preprint, arXiv:1310.8635 [math.NT], 2013-2014.
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FORMULA
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a(n) = A035263(1+floor(n/2)). - Benoit Cloitre, Mar 23 2004
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
a(n) = (A(n+2) - A(n)) mod 2, for A = A019300, A001285, A010060, A010059, A000069, A001969. - Philippe Deléham, Mar 28 2004
a(n) = A001006(n) mod 2. - Christian G. Bower, Jun 12 2005
a(n) = (-1)^n*(A096268(n+1) - A096268(n)). - Johannes W. Meijer, Feb 02 2013
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A081706.
Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.
Sequence in context: A068432 A134668 A309970 * A267537 A329670 A183919
Adjacent sequences: A039960 A039961 A039962 * A039964 A039965 A039966
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Christian G. Bower, Jun 12 2005
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe and Ralf Stephan, Jul 13 2007
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STATUS
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approved
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