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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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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; 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.
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
| F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
Index entries for sequences related to necklaces
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FORMULA
| Sum_{ d divides n } mu(d)*A000029(n/d).
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MAPLE
| 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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MATHEMATICA
| a29[n_] := a29[n] = (s = If[OddQ[n], 2^((n-1)/2) , 2^(n/2 - 2) + 2^(n/2 - 1)]; a29[0] = 1; Do[s = s + EulerPhi[d]*2^(n/d)/(2*n), {d, Divisors[n]}]; s); a[n_] := Sum[ MoebiusMu[d]*a29[n/d], {d, Divisors[n]}]; a[0] = 1; Table[ a[n], {n, 0, 34}] (* From Jean-François Alcover, Oct 04 2011 *)
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CROSSREFS
| Sequence in context: A108618 A097719 A056493 * A001037 A122086 A082594
Adjacent sequences: A001368 A001369 A001370 * A001372 A001373 A001374
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net)
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