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A209035 Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n. 1

%I

%S 6,86,576,2517,8235,22249,52208,110285,214440,390344,672932,1108883,

%T 1758433,2698447,4024458,5854361,8330650,11624758,15939472,21513945,

%U 28626249,37599103,48802532,62660333,79652814,100324030,125284570

%N Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.

%C Row 7 of A209032.

%H R. H. Hardin, <a href="/A209035/b209035.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical: a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28).

%e Some solutions for n=6:

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012

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Last modified October 28 03:12 EDT 2021. Contains 348308 sequences. (Running on oeis4.)