A039982 Let phi denote the morphism 0 -> 11, 1 -> 10. This sequence is the limit S(oo) where S(0) = 1; S(n+1) = 1.phi(S(n)).

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

Offset

0,1

Comments

An example of a d-perfect sequence.

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

Example

The first few S(i) are:
S(0) = 1
S(1) = 1.10 = 110
S(2) = 1.101011 = 1101011
S(3) = 1.10101110111010 = 110101110111010
...

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: A093719 A153778 A065251 * 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

Entry revised by N. J. A. Sloane, Feb 23 2019

Status

approved