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%I #13 Jul 07 2018 06:16:18
%S 32,609,4390,19657,65134,177097,417204,883409,1720628,3135633,5410378,
%T 8921049,14153874,21728505,32416136,47167393,67132584,93694273,
%U 128489486,173447145,230812054,303187369,393560188,505349233,642431868,809197169
%N Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.
%C Row 7 of A208825.
%H R. H. Hardin, <a href="/A208828/b208828.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 8*a(n-3) + 14*a(n-4) - 14*a(n-6) + 8*a(n-7) + 3*a(n-8) - 4*a(n-9) + a(n-10).
%F Empirical g.f.: x*(32 + 481*x + 2050*x^2 + 4180*x^3 + 4100*x^4 + 2126*x^5 + 462*x^6 + 28*x^7 - 4*x^8 + x^9) / ((1 - x)^7*(1 + x)^3). - _Colin Barker_, Jul 07 2018
%e Some solutions for n=3:
%e -3 -3 -2 -3 -3 -3 -3 -3 -3 -3 -3 -2 -3 -1 -3 -2
%e 1 -1 -2 -1 2 -2 1 -1 -2 -2 3 -2 2 -1 -1 -1
%e -1 3 0 -2 0 2 -1 1 1 -1 0 -1 -2 0 -1 1
%e -1 1 1 -1 1 1 2 1 3 2 -2 -1 0 0 1 -1
%e 1 0 2 2 -2 2 -3 1 -3 2 -2 3 1 1 1 -1
%e 2 -2 -1 3 -1 -2 1 2 3 3 1 0 0 1 2 3
%e 1 2 2 2 3 2 3 -1 1 -1 3 3 2 0 1 1
%Y Cf. A208825.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2012
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