Search: id:A000011
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%I A000011 M0312 N0114
%S A000011 1,1,2,2,4,4,8,9,18,23,44,63,122,190,362,612,1162,2056,3914,7155,13648,
               25482,
%T A000011 48734,92205,176906,337594,649532,1246863,2405236,4636390,8964800,17334801,
%U A000011 33588234,65108062,126390032,245492244,477353376,928772650,1808676326,
               3524337980
%N A000011 Number of n-bead necklaces (turning over is allowed) where complements 
               are equivalent.
%D A000011 N. J. Fine, Classes of periodic sequences, Illinois J. Math., 2 (1958), 
               285-302.
%D A000011 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois 
               J. Math., 5 (1961), 657-665.
%D A000011 W. D. Hoskins; Anne Penfold Street, Twills on a given number of harnesses, 
               J. Austral. Math. Soc. Ser. A 33 (1982), no. 1, 1-15.
%D A000011 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000011 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000011 T. D. Noe, <a href="b000011.txt">Table of n, a(n) for n = 0..200</a>
%H A000011 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A000011 H. Bottomley, <a href="A11_A13.gif">Initial terms of A000011 and A000013</
               a>
%H A000011 F. Ruskey, <a href="http://www.theory.cs.uvic.ca/~cos/inf/neck/NecklaceInfo.html">
               Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A000011 <a href="Sindx_Ne.html#necklaces">Index entries for sequences related 
               to necklaces</a>
%H A000011 <a href="Sindx_Br.html#bracelets">Index entries for sequences related 
               to bracelets</a>
%F A000011 (A000013(n)+2^[n/2])/2.
%e A000011 Contribution from Jason Orendorff (jason.orendorff(AT)gmail.com), Jan 
               09 2009: (Start)
%e A000011 The binary bracelets for small n are:
%e A000011 . n: bracelets
%e A000011 . 0: (the empty bracelet)
%e A000011 . 1: 0
%e A000011 . 2: 00, 01
%e A000011 . 3: 000, 001
%e A000011 . 4: 0000, 0001, 0011, 0101
%e A000011 . 5: 00000, 00001, 00011, 00101
%e A000011 . 6: 000000, 000001, 000011, 000101, 000111, 001001, 001011, 010101 (End)
%e A000011 The above lines illustrate the fact that to get constant-width font in 
               the Wiki version of the OEIS, you should begin each line with a dot.
%p A000011 with(numtheory): A000011 := proc(n) local s,d; if n = 0 then RETURN(1) 
               else s := 2^(floor(n/2)); for d in divisors(n) do s := s+(phi(2*d)*2^(n/
               d))/(2*n); od; RETURN(s/2); fi; end;
%t A000011 a[n_] := Fold[ #1 + EulerPhi[2#2]2^(n/#2)/(2n) &, 2^Floor[n/2], Divisors[n]]/
               2
%o A000011 (PARI) a(n)=if(n<1,!n,2^(n\2)/2+sumdiv(n,k,eulerphi(2*k)*2^(n/k))/n/4)
%Y A000011 Cf. A000013. Bisections give A000117 and A092668.
%Y A000011 Sequence in context: A060546 A163403 A120803 this_sequence A022476 A000013 
               A064484
%Y A000011 Adjacent sequences: A000008 A000009 A000010 this_sequence A000012 A000013 
               A000014
%K A000011 nonn,nice,easy
%O A000011 0,3
%A A000011 N. J. A. Sloane (njas(AT)research.att.com).
%E A000011 Better description from Christian G. Bower (bowerc(AT)usa.net). More 
               terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 13 
               2000.

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