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Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
1

%I #9 Mar 18 2018 18:31:32

%S 38,988,7974,37044,125322,344456,817362,1738516,3397474,6205668,

%T 10726862,17710724,28129694,43219580,64523202,93937312,133763354,

%U 186761160,256205942,345949192,460482450,605004348,785491674,1008773192,1282606758

%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.

%C Row 7 of A208945.

%H R. H. Hardin, <a href="/A208949/b208949.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 9*a(n-6) + 9*a(n-8) - 11*a(n-9) + 10*a(n-10) - 11*a(n-11) + 10*a(n-12) - 5*a(n-13) + a(n-14).

%e Some solutions for n=5:

%e -4 -5 -5 -3 -5 -5 -4 -5 -4 -5 -2 -5 -5 -3 -5 -5

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2012