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Search: id:A001867
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| A001867 |
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Number of n-bead necklaces with 3 colors.
(Formerly M2548 N1008)
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+0
10
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| 1, 3, 6, 11, 24, 51, 130, 315, 834, 2195, 5934, 16107, 44368, 122643, 341802, 956635, 2690844, 7596483, 21524542, 61171659, 174342216, 498112275, 1426419858, 4093181691, 11767920118, 33891544419, 97764131646, 282429537947, 817028472960
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 162.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 7.112(a).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Index entries for sequences related to necklaces
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 3
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FORMULA
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(1/n)*Sum_{d|n} phi(d)*3^(n/d), n>0.
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MAPLE
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A001867 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+phi(d)*3^(n/d); od; RETURN(s/n); fi; end;
spec := [N, {N=Cycle(bead), bead=Union(R, G, B), R=Atom, B=Atom, G=Atom}]; [seq(combstruct[count](spec, size=n), n=1..40)];
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CROSSREFS
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Cf. A054610.
Sequence in context: A088052 A045693 A051284 this_sequence A000998 A109781 A101958
Adjacent sequences: A001864 A001865 A001866 this_sequence A001868 A001869 A001870
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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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