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Search: id:A001868
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| A001868 |
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Number of n-bead necklaces with 4 colors.
(Formerly M3390 N1370)
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+0
12
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| 1, 4, 10, 24, 70, 208, 700, 2344, 8230, 29144, 104968, 381304, 1398500, 5162224, 19175140, 71582944, 268439590, 1010580544, 3817763740, 14467258264, 54975633976, 209430787824, 799645010860, 3059510616424, 11728124734500
(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.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 162.
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).
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
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 4
Index entries for sequences related to necklaces
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FORMULA
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(1/n)*Sum_{d|n} phi(d)*4^(n/d), n>0.
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MAPLE
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A001868 := proc(n) local d, s; if n = 0 then RETURN(1); else s := 0; for d in divisors(n) do s := s+phi(d)*4^(n/d); od; RETURN(s/n); fi; end;
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CROSSREFS
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Cf. A054611.
Sequence in context: A079844 A080617 A080628 this_sequence A038783 A127070 A107961
Adjacent sequences: A001865 A001866 A001867 this_sequence A001869 A001870 A001871
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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