%I #9 Mar 18 2018 17:45:17
%S 1,5,13,31,71,137,243,399,619,927,1329,1857,2525,3355,4385,5627,7121,
%T 8893,10971,13407,16213,19449,23143,27333,32083,37413,43389,50053,
%U 57447,65651,74683,84631,95537,107455,120475,134625,149997,166649,184637
%N Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
%C Row 5 of A209007.
%H R. H. Hardin, <a href="/A209009/b209009.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19).
%e Some solutions for n=6:
%e -2 -1 -3 -2 -2 -3 -2 -1 -3 -2 -3 -3 -1 -4 -4 -2
%e -1 -1 -2 1 1 -2 -1 -1 -1 0 -3 0 0 -3 1 0
%e 0 2 0 0 -1 2 2 0 3 2 1 0 1 3 4 2
%e 3 0 3 2 1 1 1 1 3 1 3 3 0 4 2 0
%e 0 0 2 -1 1 2 0 1 -2 -1 2 0 0 0 -3 0
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 04 2012