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%I #12 Mar 19 2018 04:13:02
%S 4,15,35,72,128,205,311,448,618,829,1083,1382,1734,2141,2605,3134,
%T 3730,4395,5137,5958,6860,7851,8933,10108,11384,12763,14247,15844,
%U 17556,19385,21339,23420,25630,27977,30463,33090,35866,38793,41873,45114,48518,52087
%N Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal
%C Row 4 of A209344.
%H R. H. Hardin, <a href="/A209345/b209345.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
%F Empirical g.f.: x*(4 + 3*x + 2*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, Mar 07 2018
%e Some solutions for n=10:
%e -5 -5 -9 -5 -7 -2 -9 -10 -9 -4 -7 -10 -4 -6 -7 -7
%e 1 -3 5 0 1 -1 5 5 -4 1 -1 -3 -4 1 7 -6
%e -3 -2 -5 4 4 4 -6 -3 3 0 6 10 3 -2 -7 10
%e 7 10 9 1 2 -1 10 8 10 3 2 3 5 7 7 3
%Y Cf. A209344.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 06 2012
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