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A039963 The period-doubling sequence A035263 repeated. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..104.

D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions, in Sequences and their Applications, C. Ding, T. Helleseth, and H. Niederreiter, eds., Proceedings of SETA'98 (Singapore, 1998), 308-317, 1999.

E. Rowland, R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635 [math.NT], 2013.

FORMULA

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 = A092444(n). - Christian G. Bower, Jun 12 2005

a(n) = (-1)^n*(A096268(n+1)- A096268(n)). - Johannes W. Meijer, Feb 02 2013

MATHEMATICA

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 *)

CROSSREFS

Cf. A081706.

Sequence in context: A127015 A068432 A134668 * A058840 A154269 A036987

Adjacent sequences:  A039960 A039961 A039962 * A039964 A039965 A039966

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Jun 12 2005

Edited by N. J. A. Sloane at the suggestion of Andrew Plewe and Ralf Stephan, Jul 13 2007

STATUS

approved

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Last modified December 7 11:34 EST 2016. Contains 278874 sequences.