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A209034 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.

%I A209034 #9 Mar 18 2018 17:45:45
%S A209034 4,33,144,471,1237,2798,5648,10483,18174,29863,46918,71037,104183,
%T A209034 148732,207352,283199,379766,501099,651612,836369,1060813,1331122,
%U A209034 1653894,2036531,2486878,3013693,3626176,4334533,5149447,6082684,7146500,8354355
%N A209034 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
%C A209034 Row 6 of A209032.
%H A209034 R. H. Hardin, <a href="/A209034/b209034.txt">Table of n, a(n) for n = 1..210</a>
%F A209034 Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).
%e A209034 Some solutions for n=6:
%e A209034   -4  -2  -4  -5  -4  -3  -1  -2  -3  -2  -3  -4  -4  -6  -3  -3
%e A209034   -2  -2  -2  -1  -1   1  -1  -1   0  -2  -2  -2  -3   0  -2  -2
%e A209034    3   0   1   2   2   0   2   0  -1  -1  -2  -1   1  -1   4   1
%e A209034    1  -2   4   1  -2   0  -1   3   3   1   1   4   5   1   0   4
%e A209034    0   4  -1   2   4   0  -1  -2   0   1   3   1   0   6  -1   2
%e A209034    2   2   2   1   1   2   2   2   1   3   3   2   1   0   2  -2
%K A209034 nonn
%O A209034 1,1
%A A209034 _R. H. Hardin_, Mar 04 2012