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A046211
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Number of ternary Lyndon words whose digits sum to 1 (or 2) mod 3; number of trace 1 (or 2) monic irreducible polynomials over GF(3).
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18
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1, 1, 3, 6, 16, 39, 104, 270, 729, 1960, 5368, 14742, 40880, 113828, 318864, 896670, 2532160, 7174089, 20390552, 58112088, 166037352, 475467916, 1364393896, 3922625070, 11297181456, 32588003000, 94143178827, 272342710380, 788854912240, 2287679086056, 6641649422408, 19302293185470
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OFFSET
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1,3
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COMMENTS
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Also number of ternary Lyndon words of trace 1 over GF(3).
Also number of ternary Lyndon words of trace 2 over GF(3).
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LINKS
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FORMULA
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a(n) = 1/(3*n) * Sum_{d divides n, gcd(d, 3)=1} mu(d) * 3^{n/d}.
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EXAMPLE
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a(4)= 6 = |{ 0001, 0022, 0112, 0121, 0211, 1222 }|.
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MATHEMATICA
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a[n_] := 1/(3n) DivisorSum[n, If[GCD[#, 3] == 1, MoebiusMu[#]*3^(n/#), 0] &]; Array[a, 32] (* Jean-François Alcover, Dec 07 2015 *)
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PROG
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(PARI) a(n) = 1/(3*n) * sumdiv(n, d, if(gcd(d, 3)==1, moebius(d)*3^(n/d), 0 ) ); /* Joerg Arndt, Aug 17 2012 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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