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%I #8 Mar 18 2018 22:09:13
%S 25,865,7377,35253,121117,336055,802125,1712987,3357255,6145113,
%T 10639105,17587647,27961449,42994779,64228807,93558167,133282385,
%U 186159325,255461573,345038397,459378989,603678961,783912475,1006905635,1280412799
%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
%C Row 7 of A209115.
%H R. H. Hardin, <a href="/A209119/b209119.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 7*a(n-2) + 9*a(n-3) - 11*a(n-4) + 12*a(n-5) - 12*a(n-6) + 10*a(n-7) - 6*a(n-8) + 3*a(n-9) - 3*a(n-11) + 6*a(n-12) - 10*a(n-13) + 12*a(n-14) - 12*a(n-15) + 11*a(n-16) - 9*a(n-17) + 7*a(n-18) - 4*a(n-19) + a(n-20) for n > 22.
%e Some solutions for n=6:
%e -5 -6 -5 -4 -6 -6 -5 -6 -4 -5 -4 -5 -4 -6 -6 -5
%e -3 -3 -1 -2 -5 2 -2 6 -3 -5 -2 6 -1 2 3 -1
%e -5 -2 -3 -1 -1 -2 -4 -3 -1 -4 -4 -4 -2 -1 -1 -2
%e -3 -4 0 -3 4 2 -2 -5 -1 4 6 -4 0 -1 4 6
%e 4 3 -2 6 0 4 2 -2 5 3 1 3 5 6 1 5
%e 6 6 6 0 3 -5 6 6 0 1 2 0 -1 -6 2 0
%e 6 6 5 4 5 5 5 4 4 6 1 4 3 6 -3 -3
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 05 2012
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