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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
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
KEYWORD
nonn
AUTHOR
Frank Ruskey, Dec 13 1999
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)