cp's OEIS Frontend

A209347 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

%I A209347 #15 Jul 09 2018 10:53:20
%S A209347 14,146,770,2698,7358,16968,34720,64942,113288,186906,294616,447084,
%T A209347 657006,939270,1311146,1792454,2405742,3176460,4133144,5307578,
%U A209347 6734984,8454190,10507808,12942408,15808702,19161706,23060930,27570546,32759566
%N A209347 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
%C A209347 Row 6 of A209344.
%H A209347 R. H. Hardin, <a href="/A209347/b209347.txt">Table of n, a(n) for n = 1..210</a>
%F A209347 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) - 5*a(n-7) + 4*a(n-8) - a(n-9).
%F A209347 Empirical g.f.: 2*x*(7 + 45*x + 128*x^2 + 167*x^3 + 128*x^4 + 48*x^5 + 5*x^6) / ((1 - x)^6*(1 + x)*(1 + x + x^2)). - _Colin Barker_, Jul 09 2018
%e A209347 Some solutions for n=8:
%e A209347   -5  -8  -6  -2  -4  -6  -6  -3  -3  -8  -8  -6  -5  -4  -5  -8
%e A209347   -4   1  -1  -2  -1  -5  -3  -1  -1   0  -3  -1   1  -2   2  -7
%e A209347   -2  -2   4   0   5  -2   5   1   2  -4   7   1  -2   1   4   8
%e A209347    4   3  -4   0  -4   2   5   2  -3  -2   3   3  -3   2   0   6
%e A209347    7   1  -1   1   4   3  -5  -3   1   7  -7  -3   7   3  -4   3
%e A209347    0   5   8   3   0   8   4   4   4   7   8   6   2   0   3  -2
%Y A209347 Cf. A209344.
%K A209347 nonn
%O A209347 1,1
%A A209347 _R. H. Hardin_, Mar 06 2012