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%I #9 Mar 18 2018 18:34:10
%S 1,3,9,19,40,77,130,213,325,484,687,956,1294,1715,2233,2863,3612,4508,
%T 5551,6779,8186,9814,11667,13773,16153,18832,21824,25171,28874,32991,
%U 37513,42502,47963,53938,60455,67549,75241,83587,92589,102325,112783
%N Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.
%C Row 5 of A208970.
%H R. H. Hardin, <a href="/A208972/b208972.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=5:
%e -3 -3 -2 -2 -3 -2 -1 -1 -1 -3 -2 -2 -2 -3 -1 -2
%e -2 -1 -2 -2 -3 -2 -1 0 0 -1 0 -1 0 -2 -1 -2
%e 1 1 -2 0 2 1 0 0 1 2 -1 0 0 2 0 -1
%e 3 3 3 3 2 1 2 1 -1 3 2 2 2 2 0 3
%e 1 0 3 1 2 2 0 0 1 -1 1 1 0 1 2 2
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 03 2012
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