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A032164
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Number of aperiodic necklaces of n beads of 6 colors; dimensions of free Lie algebras.
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6
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1, 6, 15, 70, 315, 1554, 7735, 39990, 209790, 1119720, 6045837, 32981550, 181394535, 1004668770, 5597420295, 31345665106, 176319264240, 995685849690, 5642219252460, 32071565263710, 182807918979777
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 79.
G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
C. G. Bower, Transforms (2)
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
Index entries for sequences related to Lyndon words
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FORMULA
| "CHK" (necklace, identity, unlabeled) transform of 6, 0, 0, 0...
Sum mu(d)*6^(n/d)/n; d|n.
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MATHEMATICA
| f[d_] := MoebiusMu[d]*6^(n/d)/n; a[n_] := Total[f /@ Divisors[n]]; a[0] = 1; Table[a[n], {n, 0, 20}](* From Jean-François Alcover, Nov 07 2011 *)
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CROSSREFS
| Cf. A001037.
Cf. A054721.
Sequence in context: A012294 A069750 A035077 * A177122 A108540 A165570
Adjacent sequences: A032161 A032162 A032163 * A032165 A032166 A032167
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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