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A001868
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Number of n-bead necklaces with 4 colors.
(Formerly M3390 N1370)
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13
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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; 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.
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
| 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
| (1/n)*Sum_{d|n} phi(d)*4^(n/d), n>0.
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MAPLE
| 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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MATHEMATICA
| a[n_] := (1/n)*Total[ EulerPhi[#]*4^(n/#) & /@ Divisors[n]]; a[0] = 1; Table[a[n], {n, 0, 24}] (* From Jean-François Alcover, Oct 21 2011 *)
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CROSSREFS
| Cf. A054611.
Sequence in context: A080617 A080628 A190169 * A038783 A127070 A107961
Adjacent sequences: A001865 A001866 A001867 * A001869 A001870 A001871
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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