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%I #9 Mar 18 2018 18:35:02
%S 15,458,3740,17771,60778,168453,401634,857433,1679810,3074315,5321674,
%T 8796771,13984178,21501971,32119660,46785813,66648788,93089119,
%U 127741326,172532039,229703658,301856427,391974770,503474661,640230118,806627193
%N Number of 7-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 7 of A209485.
%H R. H. Hardin, <a href="/A209488/b209488.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-3) - a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-9) - a(n-13) - 2*a(n-14) + 2*a(n-15) - a(n-16) + a(n-17) + a(n-19) - 2*a(n-21) + a(n-22) for n > 24.
%e Some solutions for n=5:
%e -3 -4 -4 -4 -4 -4 -2 -5 -4 -4 -5 -4 -4 -5 -4 -5
%e -1 -1 -4 -3 0 -3 -1 -4 -4 -2 5 2 -2 -4 1 -1
%e -2 0 2 4 -1 -1 -2 5 -4 2 -4 3 0 5 1 3
%e 4 -2 2 -3 4 -1 0 3 2 1 -2 -3 1 0 -3 -5
%e -3 3 3 4 0 4 3 -5 5 -3 -2 -1 4 1 1 4
%e 0 4 -3 1 1 5 -2 1 1 3 3 -1 -1 -1 1 5
%e 5 0 4 1 0 0 4 5 4 3 5 4 2 4 3 -1
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 09 2012
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