%I #13 Jul 08 2018 10:48:08

%S 19,265,1465,5239,14431,33469,68723,128845,225127,371859,586669,

%T 890881,1309873,1873417,2616037,3577367,4802491,6342301,8253855,

%U 10600717,13453315,16889299,20993881,25860193,31589645,38292265,46087057,55102359

%N Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.

%C Row 6 of A209073.

%H R. H. Hardin, <a href="/A209075/b209075.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8) for n > 9.

%F Empirical g.f.: x*(19 + 170*x + 330*x^2 + 355*x^3 + 161*x^4 + 30*x^5 - 16*x^6 + 9*x^7 - 2*x^8) / ((1 - x)^6*(1 + x + x^2)). - _Colin Barker_, Jul 08 2018

%e Some solutions for n=6:

%e -4 -5 -4 -5 -5 -5 -4 -3 -5 -5 -5 -5 -5 -6 -6 -5

%e 3 -2 4 -1 -1 -3 3 2 1 5 -1 -1 -5 6 2 5

%e 1 5 3 -2 4 -1 -3 -2 0 0 4 4 5 2 4 0

%e 1 -4 -1 6 -2 3 3 -1 4 -4 -2 -4 6 -4 1 -2

%e -3 4 -2 4 -2 2 -2 1 0 5 -1 6 -5 6 3 -4

%e 2 2 0 -2 6 4 3 3 0 -1 5 0 4 -4 -4 6

%Y Cf. A209073.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012