cp's OEIS Frontend

A274018 Number of n-bead ternary necklaces (no turning over allowed) that avoid the subsequence 110.

%I A274018 #43 Jun 24 2018 18:34:05
%S A274018 1,3,6,10,21,42,103,237,603,1519,3942,10257,27131,71940,192462,516933,
%T A274018 1395636,3781356,10283911,28050600,76732047,210414811,578330649,
%U A274018 1592821005,4395261552,12149386569,33637309323,93267459520,258961863288,719938597227,2003881480452,5583818718102,15575529493713
%N A274018 Number of n-bead ternary necklaces (no turning over allowed) that avoid the subsequence 110.
%C A274018 The pattern in this enumeration must be contiguous (all three values next to each other in one sequence of three letters).
%H A274018 Math Stackexchange, Marko Riedel et al., <a href="http://math.stackexchange.com/questions/1812920/">Counting circular sequences</a>.
%H A274018 Marko Riedel, <a href="/A274017/a274017.maple.txt">Maple code for this sequence</a>.
%F A274018 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 A274018 a(n) = (1/n)*Sum_{d|n} phi(n/d)*A215885(d) for n >= 1. - _Petros Hadjicostas_, Sep 13 2017
%e A274018 The necklace
%e A274018     1--1
%e A274018    /    \
%e A274018   0      0
%e A274018   |      |
%e A274018   1      2
%e A274018    \    /
%e A274018     0--0
%e A274018 contains one instance of the subsequence starting in the upper left corner. Unlike a bracelet, the necklace is oriented.
%Y A274018 Cf. A000031, A274017, A274019, A274020.
%K A274018 nonn
%O A274018 0,2
%A A274018 _Marko Riedel_, Jun 06 2016