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A209117 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2. 1

%I #13 Jul 08 2018 21:30:59

%S 5,63,261,741,1683,3325,5935,9835,15397,23039,33209,46421,63227,84225,

%T 110055,141411,179025,223687,276217,337489,408427,490001,583211,

%U 689123,808841,943515,1094337,1262553,1449447,1656361,1884667,2135791,2411209

%N Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

%C Row 5 of A209115.

%H R. H. Hardin, <a href="/A209117/b209117.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).

%F Empirical g.f.: x*(5 + 48*x + 87*x^2 + 137*x^3 + 127*x^4 + 103*x^5 + 39*x^6 + 5*x^7 + 2*x^8 - x^9) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 08 2018

%e Some solutions for n=6:

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

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

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

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

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

%Y Cf. A209115.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 05 2012

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)