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A209488 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.

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