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Search: id:A000046
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| A000046 |
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Number of primitive n-bead necklaces (turning over is allowed) where complements are equivalent.
(Formerly M0696 N0257)
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4
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| 1, 1, 1, 1, 2, 3, 5, 8, 14, 21, 39, 62, 112, 189, 352, 607, 1144, 2055, 3885, 7154, 13602, 25472, 48670, 92204, 176770, 337590, 649341, 1246840, 2404872, 4636389, 8964143, 17334800, 33587072, 65107998, 126387975, 245492232, 477349348
(list; graph; listen)
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OFFSET
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0,5
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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.
B. Gruenbaum and G. C. Shephard, The geometry of fabrics, pp. 77-98 of F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. Pitman, Boston, 1984.
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LINKS
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Christian G. Bower, Table of n, a(n) for n = 0..1000
Index entries for sequences related to necklaces
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FORMULA
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Sum_{ d divides n } mu(d)*A000011(n/d).
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MAPLE
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with(numtheory); A000046 := proc(n) local s, d; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+mobius(d)*A000011(n/d); od; RETURN(s); fi; end;
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CROSSREFS
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Similar to A000011, but counts primitive necklaces.
Cf. A054199.
Adjacent sequences: A000043 A000044 A000045 this_sequence A000047 A000048 A000049
Sequence in context: A034413 A034416 A056366 this_sequence A131132 A004692 A094926
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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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