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%I #13 Jul 07 2018 08:51:06
%S 8,68,274,766,1722,3376,6004,9928,15514,23178,33378,46624,63464,84496,
%T 110366,141766,179426,224132,276712,338040,409034,490662,583934,
%U 689912,809696,944436,1095330,1263622,1450594,1657584,1885972,2137184,2412690
%N Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
%C Row 5 of A208945.
%H R. H. Hardin, <a href="/A208947/b208947.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) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).
%F Empirical g.f.: 2*x*(4 + 22*x + 47*x^2 + 66*x^3 + 63*x^4 + 48*x^5 + 21*x^6 + 6*x^7 - x^8) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 07 2018
%e Some solutions for n=5:
%e -5 -3 -4 -4 -5 -5 -5 -5 -3 -4 -5 -5 -4 -5 -2 -4
%e 0 2 2 2 -5 4 5 -5 1 -2 4 3 1 -3 4 0
%e 5 -2 3 -2 3 -2 -1 3 -2 2 2 3 3 2 -1 5
%e -2 4 2 5 5 2 -4 2 5 5 1 0 -2 1 0 1
%e 2 -1 -3 -1 2 1 5 5 -1 -1 -2 -1 2 5 -1 -2
%Y Cf. A208945.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 03 2012
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