%I #9 Mar 18 2018 17:54:58

%S 9,155,1111,4935,16307,44209,104001,219929,428031,779487,1344353,

%T 2215747,3514415,5393753,8045199,11704103,16655941,23243017,31871521,

%U 43019059,57242537,75186543,97592047,125305621,159288983,200629037,250548251

%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.

%C Row 7 of A208993.

%H R. H. Hardin, <a href="/A208998/b208998.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) - a(n-6) + a(n-8) + a(n-9) + a(n-10) + a(n-12) - a(n-13) - a(n-15) - a(n-16) - a(n-17) + a(n-19) + 2*a(n-20) + a(n-21) - a(n-22) - a(n-23) - a(n-24) + a(n-25).

%e Some solutions for n=6:

%e -5 -5 -2 -6 -6 -3 -4 -2 -2 -5 -4 -3 -5 -6 -4 -4

%e 0 0 -1 -1 0 -2 1 1 2 1 -1 -1 -1 -3 -4 -2

%e 3 3 1 2 3 4 -2 0 1 0 -2 0 1 2 1 0

%e 0 4 1 3 5 -2 1 0 -1 -2 2 3 -1 2 -1 4

%e 1 0 -2 6 3 1 3 0 0 1 0 1 2 1 4 3

%e 3 1 2 0 -1 1 0 2 0 5 5 1 4 5 3 -3

%e -2 -3 1 -4 -4 1 1 -1 0 0 0 -1 0 -1 1 2

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012