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 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)). 6
 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 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. 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 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

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Last modified June 6 17:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)