A209076 - OEIS

%I #9 Mar 19 2018 04:10:25

%S 39,1007,8008,37108,125428,344618,817594,1738838,3397900,6206228,

%T 10727576,17711618,28130798,43220926,64524812,93939228,133765612,

%U 186763798,256208998,345952710,460486468,605008920,785496844,1008779010

%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.

%C Row 7 of A209073.

%H R. H. Hardin, <a href="/A209076/b209076.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 11*a(n-2) + 16*a(n-3) - 20*a(n-4) + 22*a(n-5) - 19*a(n-6) + 11*a(n-7) - 11*a(n-9) + 19*a(n-10) - 22*a(n-11) + 20*a(n-12) - 16*a(n-13) + 11*a(n-14) - 5*a(n-15) + a(n-16) for n > 18.

%e Some solutions for n=6:

%e   -4  -5  -4  -6  -5  -6  -5  -6  -6  -6  -4  -6  -5  -5  -6  -5

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

%e   -2   2   1   2   1   1   2   0   2   5   4   2   6   6   4  -5

%e    6   4   5   6   4   6   3   4   5   6   3   5   3   1   5   4

%e    2  -2   6  -1   3   3   2   5  -4   0  -3   0  -4  -4   1   2

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012