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Search: id:A032164
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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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+0
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; listen)
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OFFSET
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0,2
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REFERENCES
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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
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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
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"CHK" (necklace, identity, unlabeled) transform of 6, 0, 0, 0...
Sum mu(d)*6^(n/d)/n; d|n.
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CROSSREFS
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Cf. A001037.
Cf. A054721.
Sequence in context: A012294 A069750 A035077 this_sequence A108540 A165570 A096565
Adjacent sequences: A032161 A032162 A032163 this_sequence A032165 A032166 A032167
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net)
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