%I #43 Jun 24 2018 18:34:05
%S 1,3,6,10,21,42,103,237,603,1519,3942,10257,27131,71940,192462,516933,
%T 1395636,3781356,10283911,28050600,76732047,210414811,578330649,
%U 1592821005,4395261552,12149386569,33637309323,93267459520,258961863288,719938597227,2003881480452,5583818718102,15575529493713
%N Number of n-bead ternary necklaces (no turning over allowed) that avoid the subsequence 110.
%C The pattern in this enumeration must be contiguous (all three values next to each other in one sequence of three letters).
%H Math Stackexchange, Marko Riedel et al., <a href="http://math.stackexchange.com/questions/1812920/">Counting circular sequences</a>.
%H Marko Riedel, <a href="/A274017/a274017.maple.txt">Maple code for this sequence</a>.
%F G.f.: 1 - Sum_{n>=1} (phi(n)/n)*log(x^(3*n) - q*x^n + 1), where q=3 is the number of symbols in the alphabet we are using. - _Petros Hadjicostas_, Sep 12 2017
%F a(n) = (1/n)*Sum_{d|n} phi(n/d)*A215885(d) for n >= 1. - _Petros Hadjicostas_, Sep 13 2017
%e The necklace
%e 1--1
%e / \
%e 0 0
%e | |
%e 1 2
%e \ /
%e 0--0
%e contains one instance of the subsequence starting in the upper left corner. Unlike a bracelet, the necklace is oriented.
%Y Cf. A000031, A274017, A274019, A274020.
%K nonn
%O 0,2
%A _Marko Riedel_, Jun 06 2016