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%I #16 Mar 19 2021 09:52:51
%S 11,136,731,2606,7179,16660,34233,64220,112263,185506,292759,444680,
%T 653957,935472,1306483,1786806,2398979,3168444,4123729,5296612,
%U 6722303,8439626,10491183,12923536,15787389,19137752,23034123,27540670,32726395
%N Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
%C Row 6 of A209485.
%H R. H. Hardin, <a href="/A209487/b209487.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.
%e Some solutions for n=8:
%e -6 -8 -6 -7 -8 -7 -7 -8 -8 -4 -5 -6 -8 -8 -6 -8
%e -1 -3 -6 -6 -2 0 -5 0 -4 -3 3 -2 1 -2 -3 3
%e 2 -1 0 6 6 6 2 -2 -5 6 -2 3 -4 7 -4 -4
%e -2 -1 -3 2 -1 -7 5 -3 8 -3 -4 6 -3 -4 4 6
%e 6 6 7 4 6 6 6 5 8 -4 2 -3 8 4 1 -1
%e 1 7 8 1 -1 2 -1 8 1 8 6 2 6 3 8 4
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 09 2012
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