%I A080846
%S A080846 0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,
%T A080846 0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,
%U A080846 1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1
%N A080846 Fixed point of the morphism 0->010, 1->011, starting from a(1) = 0.
%C A080846 A cube-free word.
%C A080846 A generalized choral sequence c(3n+r_0)=0, c(3n+r_1)=1, c(3n+r_c)=c(n), 
               with r_0=0, r_1=1, and r_c=2. [From Joel Reyes Noche (joel.noche(AT)up.edu.ph), 
               Jul 09 2009]
%D A080846 J. Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. 
               EATCS, #79 (2003), pp. 178-228.
%D A080846 J. R. Noche, Generalized Choral Sequences, Matimyas Matematika, 31(2008), 
               25-28. [From Joel Reyes Noche (joel.noche(AT)up.edu.ph), Jul 09 2009]
%H A080846 Jean Berstel, <a href="http://www-igm.univ-mlv.fr/~berstel/">Home Page</
               a>
%F A080846 a(n) = (A062756(n) - A062756(n+1) + 1)/2, where A062756(n) is the number 
               of 1's in the ternary expansion of n. From formula in A062756: G.f.: 
               A(x) = 1/(1-x)/2 - Sum_{k>=0} x^(3^k-1)/(1+x^(3^k)+x^(2*3^k))/2. 
               - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 24 2006
%F A080846 Given G.f. A(x) then B(x) = x * A(x) satisfies B(x) = x^2 / (1 - x^3) 
               + B(x^3). - Michael Somos Jul 29 2009
%F A080846 a(3*n) = 0, a(3*n + 1) = 1, a(3*n - 1) = a(n - 1). - Michael Somos Jul 
               29 2009
%t A080846 Nest[Flatten[ # /. {0 -> {0, 1, 0}, 1 -> {0, 1, 1}}] &, {0}, 5]
%o A080846 (PARI) {a(n)=if(n<1,0,polcoeff(1/(1-x)/2-sum(k=0,ceil(log(n+1)/log(3)), 
               x^(3^k-1)/(1+x^(3^k)+x^(2*3^k)+x*O(x^n)))/2,n))} - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Feb 24 2006
%o A080846 (PARI) {a(n) = if( n<1, 0, n++; n / 3^valuation(n, 3) % 3 -1 )} /* Michael 
               Somos Jul 29 2009 */ - Michael Somos Jul 29 2009
%Y A080846 See A060236 for another version.
%Y A080846 Cf. A062756.
%Y A080846 Sequence in context: A078580 A059651 A084091 this_sequence A082401 A157238 
               A059448
%Y A080846 Adjacent sequences: A080843 A080844 A080845 this_sequence A080847 A080848 
               A080849
%K A080846 nonn,easy
%O A080846 0,1
%A A080846 N. J. A. Sloane (njas(AT)research.att.com), Mar 29 2003
%E A080846 More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 
               01 2003