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Search: id:A080846
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| A080846 |
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Fixed point of the morphism 0->010, 1->011, starting from a(1) = 0. |
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+0
4
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A cube-free word.
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]
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REFERENCES
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J. Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. EATCS, #79 (2003), pp. 178-228.
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]
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LINKS
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Jean Berstel, Home Page
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FORMULA
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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
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
a(3*n) = 0, a(3*n + 1) = 1, a(3*n - 1) = a(n - 1). - Michael Somos Jul 29 2009
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MATHEMATICA
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Nest[Flatten[ # /. {0 -> {0, 1, 0}, 1 -> {0, 1, 1}}] &, {0}, 5]
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PROGRAM
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(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
(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
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CROSSREFS
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See A060236 for another version.
Cf. A062756.
Sequence in context: A078580 A059651 A084091 this_sequence A082401 A157238 A059448
Adjacent sequences: A080843 A080844 A080845 this_sequence A080847 A080848 A080849
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 29 2003
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EXTENSIONS
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More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 01 2003
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