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 A046211 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). 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also number of ternary Lyndon words of trace 1 over GF(3). Also number of ternary Lyndon words of trace 2 over GF(3). LINKS G. C. Greubel, Table of n, a(n) for n = 1..2000 F. Ruskey, Number of q-ary Lyndon words with given trace mod q F. Ruskey, Number of monic irreducible polynomials over GF(q) with given trace F. Ruskey, Number of Lyndon words over GF(q) with given trace Index entries for sequences related to Lyndon words FORMULA a(n) = 1/(3*n) * Sum_{d divides n, gcd(d, 3)=1} mu(d) * 3^{n/d}. a(n) ~ 3^(n-1) / n. - Vaclav Kotesovec, Apr 18 2016 EXAMPLE a(4)= 6 = |{ 0001, 0022, 0112, 0121, 0211, 1222 }|. MATHEMATICA a[n_] := 1/(3n) DivisorSum[n, If[GCD[#, 3] == 1, MoebiusMu[#]*3^(n/#), 0] &]; Array[a, 32] (* Jean-François Alcover, Dec 07 2015 *) PROG (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 */ CROSSREFS Cf. A008683 (mu), A046209. Sequence in context: A248091 A168317 A188442 * A239980 A205770 A301959 Adjacent sequences: A046208 A046209 A046210 * A046212 A046213 A046214 KEYWORD nonn AUTHOR Frank Ruskey, Dec 13 1999 STATUS approved

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Last modified December 8 14:49 EST 2023. Contains 367680 sequences. (Running on oeis4.)