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 A046209 Number of ternary Lyndon words whose digits sum to 0 mod 3; also number of trace 0 irreducible polynomials over GF(3). 11
 1, 1, 2, 6, 16, 38, 104, 270, 726, 1960, 5368, 14736, 40880, 113828, 318848, 896670, 2532160, 7174050, 20390552, 58112088, 166037248, 475467916, 1364393896, 3922624800, 11297181456, 32588003000, 94143178098, 272342710380, 788854912240, 2287679084096, 6641649422408, 19302293185470 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also number of ternary Lyndon words of trace 0 over GF(3). LINKS G. C. Greubel, Table of n, a(n) for n = 1..2000 FORMULA a(n) = 1/(3*n) * sum(d divides n, gcd(d, 3)*mu(d)*3^(n/d) ). EXAMPLE a(4) = 6 = |{ 0012, 0021, 0111, 0102, 0222, 1122 }|. MATHEMATICA a[n_] := 1/(3n) DivisorSum[n, GCD[#, 3]*MoebiusMu[#]*3^(n/#)&]; Array[a, 32] (* Jean-François Alcover, Dec 06 2015, adapted from PARI *) PROG (PARI) a(n) = 1/(3*n) * sumdiv(n, d, gcd(d, 3)*moebius(d)*3^(n/d) ); /* Joerg Arndt, Aug 17 2012 */ CROSSREFS Cf. A046211. Sequence in context: A265758 A265107 A217631 * A285885 A273348 A198951 Adjacent sequences:  A046206 A046207 A046208 * A046210 A046211 A046212 KEYWORD nonn AUTHOR Frank Ruskey, Dec 13 1999 STATUS approved

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Last modified October 27 15:27 EDT 2020. Contains 338035 sequences. (Running on oeis4.)