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A046211
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Number of ternary Lyndon words whose digits sum to 1 mod 3; number of ternary Lyndon words whose digits sum to 2 mod 3; number of trace 1 (or 2) monic irreducible polynomials over GF(3).
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12
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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).
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LINKS
| Index entries for sequences related to Lyndon words
F. Ruskey, Number of q-ary Lyndon words with given trace mod q
F. Ruskey, Number of monic irreducible polynomials over GF(q) with zero trace ...
F. Ruskey, Number of Lyndon words of given trace
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FORMULA
| ( Sum_{d|n, gcd(d, 3)=1} mu(d)*3^{n/d}) / (3n)
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EXAMPLE
| a(4)= 6 = |{ 0001, 0022, 0112, 0121, 0211, 1222 }|
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CROSSREFS
| Cf. A046209.
Sequence in context: A001675 A168317 A188442 * A205770 A018022 A166536
Adjacent sequences: A046208 A046209 A046210 * A046212 A046213 A046214
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KEYWORD
| nonn
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AUTHOR
| Frank Ruskey (ruskey(AT)cs.uvic.ca), Dec 13 1999
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