%I
%S 1,1,2,3,6,9,22,40,100,225,582,1464,3960,10585,29252,80819,226530,
%T 636321,1800562,5107480,14548946,41538916,118929384,341187048,
%U 980842804,2824561089,8147557742,23536592235,68087343148,197216119545,571924754778,1660419530056,4825588205920
%N Number of bracelet structures using a maximum of three different colored beads.
%C Turning over will not create a new bracelet. Permuting the colors of the beads will not change the structure.
%D M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%H Andrew Howroyd, <a href="/A056353/b056353.txt">Table of n, a(n) for n = 0..200</a>
%H R. M. Thompson and R. T. Downs, <a href="http://www.geo.arizona.edu/xtal//group/pdf/acB57766.pdf">Systematic generation of all nonequivalent closest packed stacking sequences of length N using group theory</a>, Acta Cryst. B57 (2001), 766771; B58 (2002), 153.
%F Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.
%F a(n) = Sum_{k=1..3} A152176(n, k) for n > 0.  _Andrew Howroyd_, Oct 25 2019
%Y Cf. A002076, A000011, A027671, A114438, A152176.
%K nonn
%O 0,3
%A _Marks R. Nester_
%E a(0)=1 prepended and terms a(28) and beyond from _Andrew Howroyd_, Oct 25 2019
