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%I #11 Jul 10 2018 06:00:16
%S 4,38,140,390,866,1702,3014,4984,7774,11620,16716,23352,31768,42302,
%T 55232,70950,89774,112150,138434,169120,204610,245452,292080,345096,
%U 404980,472382,547820,631998,725474,829006,943190,1068832,1206574
%N Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
%C Row 5 of A209485.
%H R. H. Hardin, <a href="/A209486/b209486.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).
%F Empirical g.f.: 2*x*(2 + 15*x + 32*x^2 + 57*x^3 + 62*x^4 + 59*x^5 + 34*x^6 + 13*x^7 + 2*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 10 2018
%e Some solutions for n=10:
%e -8 -5 -10 -6 -7 -6 -7 -8 -9 -7 -6 -10 -9 -8 -9 -6
%e -7 -4 1 -2 -4 0 -5 -5 9 -2 0 1 -1 0 2 -5
%e 2 9 3 6 -5 -6 0 2 -7 6 4 -6 7 4 -7 1
%e 3 -5 -4 -3 6 4 2 3 -3 2 0 7 2 -2 10 2
%e 10 5 10 5 10 8 10 8 10 1 2 8 1 6 4 8
%Y Cf. A209485.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 09 2012
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