%I A115117
%S A115117 1,2,7,20,68,224,780,2720,9709,34918,127100,465920,1720740,6390930,
%T A115117 23860928,89477120,336860180,1272578048,4822419420,18325176316,
%U A115117 69810262080,266548209850,1019836872140,3909374443520,15011998757888
%N A115117 Number of primitive (aperiodic, or Lyndon) 3-asymmetric rhythm cycles: 
               ones having no nontrivial shift automorphism. 3-Asymmetric rhythm 
               cycles (A115115): binary necklaces of length 3n subject to the restriction 
               that for any k if the k-th bead is of color 1 then the (k+n)-th and 
               (k+2n)-th beads (modulo 3n) are of color 0.
%H A115117 R. W. Hall and P. Klingsberg, <a href="http://www.sju.edu/%7Erhall/Rhythms/
               asymmetric.pdf">Asymmetric Rhythms, Tiling Canons and Burnside's 
               Lemma</a>,Bridges Proceedings, pp. 189-194, 2004 (Winfield, Kansas).
%H A115117 R. W. Hall and P. Klingsberg, <a href="http://www.sju.edu/%7Erhall/Rhythms/
               AsymmetricRhythms/canons.pdf">Asymmetric Rhythms and Tiling Canons</
               a>, Preprint, 2004.
%F A115117 a(n)=(Sum_{d|n}phi(3d)+Sum_{d|n, (3, d)=1}mu(d)4^(n/d))/(3n), where mu(n) 
               is the Moebius function A008683.
%Y A115117 Cf. A006575, A115115.
%Y A115117 Sequence in context: A055891 A122877 A000150 this_sequence A029890 A095268 
               A118397
%Y A115117 Adjacent sequences: A115114 A115115 A115116 this_sequence A115118 A115119 
               A115120
%K A115117 easy,nonn
%O A115117 1,2
%A A115117 Valery A. Liskovets (liskov(AT)im.bas-net.by), Jan 17 2006