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 A209347 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal. 1

%I

%S 14,146,770,2698,7358,16968,34720,64942,113288,186906,294616,447084,

%T 657006,939270,1311146,1792454,2405742,3176460,4133144,5307578,

%U 6734984,8454190,10507808,12942408,15808702,19161706,23060930,27570546,32759566

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

%C Row 6 of A209344.

%H R. H. Hardin, <a href="/A209347/b209347.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=8:

%e -5 -8 -6 -2 -4 -6 -6 -3 -3 -8 -8 -6 -5 -4 -5 -8

%e -4 1 -1 -2 -1 -5 -3 -1 -1 0 -3 -1 1 -2 2 -7

%e -2 -2 4 0 5 -2 5 1 2 -4 7 1 -2 1 4 8

%e 4 3 -4 0 -4 2 5 2 -3 -2 3 3 -3 2 0 6

%e 7 1 -1 1 4 3 -5 -3 1 7 -7 -3 7 3 -4 3

%e 0 5 8 3 0 8 4 4 4 7 8 6 2 0 3 -2

%Y Cf. A209344.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 06 2012

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Last modified December 5 18:48 EST 2021. Contains 349557 sequences. (Running on oeis4.)