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A039982 An example of a d-perfect sequence. 4
1, 1, 0, 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Concatenation of the bit sequences forming A035263. - David Callan, Oct 08 2005

Image, under the coding a,b,d -> 1, c -> 0, of the fixed point, starting with a, of the morphism a -> ab, b -> cd, c -> cd, d -> bb. - Jeffrey Shallit, May 15 2016

LINKS

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

Martin Klazar and Florian Luca, On integrality and periodicity of the Motzkin numbers.

Martin Klazar and Florian Luca, On integrality and periodicity of the Motzkin numbers, Aequationes Math. 69 (2005), no. 1-2, 68-75.

D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions

D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions, Sequences and their Applications, Discrete Mathematics and Theoretical Computer Science 1999, pp 308-317.

FORMULA

a(n) = A090344(n) mod 2. - Christian G. Bower, Jun 12 2005

a(n) = M(2n) mod 2 where M(n) is the Motzkin number A001006. - David Callan, Oct 08 2005

MATHEMATICA

substitutionRule={1->{1, 0}, 0->{1, 1}}; makeSubstitution[seq_]:=Flatten[seq/.substitutionRule]; Flatten[NestList[makeSubstitution, {1}, 5]]

NestList[Flatten[ # /. {0 -> {1, 1}, 1 -> {1, 0}}] &, {1}, 6] // Flatten (* Robert G. Wilson v, Mar 29 2006 *)

PROG

(PARI) a(n)=my(A=1+x); for(i=1, n, A=1/(1-x+x*O(x^n))+x^2*A^2+x*O(x^n)); polcoeff(A, n)%2 \\ Charles R Greathouse IV, Feb 04 2013

CROSSREFS

Cf. A001006, A035263, A090344.

Sequence in context: A093719 A153778 A065251 * A131372 A098457 A137161

Adjacent sequences:  A039979 A039980 A039981 * A039983 A039984 A039985

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Jun 12 2005

STATUS

approved

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Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)