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A039982 An example of a d-perfect sequence. 5
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

0

COMMENTS

Concatenation of the bit sequences 1, 10, 1011, 10111010, 1011101010111011, ... used in a construction of A035263 (see Comment there by Benoit Cloitre). - 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

Antti Karttunen, Table of n, a(n) for n = 0..65537

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.

Index entries for characteristic functions

FORMULA

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

(PARI)

up_to = 16384;

A090344list(up_to) = { my(v=vector(up_to)); v[1] = 1; v[2] = 2; v[3] = 3; for(n=4, up_to, v[n] = ((2*n+2)*v[n-1] -(4*n-6)*v[n-3] +(3*n-4)*v[n-2])/(n+2)); (v); };

v090344 = A090344list(up_to);

A090344(n) = if(!n, 1, v090344[n]);

A039982(n) = (A090344(n)%2); \\ Antti Karttunen, Sep 27 2018

(GAP) b:=[1, 1, 2];; for n in [4..120] do b[n]:=(1/(n+1))* (2*n*b[n-1]+(3*n-7)*b[n-2]-(4*n-10)*b[n-3]);; od; a:=b mod 2; # Muniru A Asiru, Sep 28 2018

CROSSREFS

Cf. A001006, A035263, A090344.

Sequence in context: A285952 A286064 A285518 * A267349 A254651 A267579

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

Offset corrected from 1 to 0 by Antti Karttunen, Sep 27 2018

STATUS

approved

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Last modified November 16 08:56 EST 2018. Contains 317268 sequences. (Running on oeis4.)