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Search: id:A001371
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| A001371 |
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Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is allowed.
(Formerly M0115 N0045)
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+0
8
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| 1, 2, 1, 2, 3, 6, 8, 16, 24, 42, 69, 124, 208, 378, 668, 1214, 2220, 4110, 7630, 14308, 26931, 50944, 96782, 184408, 352450, 675180, 1296477, 2493680, 4805388, 9272778, 17919558, 34669600, 67156800, 130215996, 252741255
(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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
Index entries for sequences related to necklaces
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FORMULA
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Sum_{ d divides n } mu(d)*A000029(n/d).
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MAPLE
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with(numtheory); A001371 := proc(n) local s, d; if n = 0 then RETURN(1) else s := 0; for d in divisors(n) do s := s+mobius(d)*A000029(n/d); od; RETURN(s); fi; end;
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CROSSREFS
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Sequence in context: A108618 A097719 A056493 this_sequence A001037 A122086 A082594
Adjacent sequences: A001368 A001369 A001370 this_sequence A001372 A001373 A001374
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net)
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