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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
5, 63, 261, 741, 1683, 3325, 5935, 9835, 15397, 23039, 33209, 46421, 63227, 84225, 110055, 141411, 179025, 223687, 276217, 337489, 408427, 490001, 583211, 689123, 808841, 943515, 1094337, 1262553, 1449447, 1656361, 1884667, 2135791, 2411209
OFFSET
1,1
COMMENTS
Row 5 of A209115.
LINKS
FORMULA
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).
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
EXAMPLE
Some solutions for n=6:
-5 -6 -3 -5 -6 -6 -6 -6 -5 -5 -4 -3 -1 -4 -4 -4
-2 4 -1 3 1 -6 -1 2 -4 3 4 -1 -1 -3 -2 0
6 -6 -2 -1 1 5 1 6 0 -3 -2 1 1 1 5 4
-5 4 5 6 5 2 6 3 4 0 3 0 0 4 -3 3
6 4 1 -3 -1 5 0 -5 5 5 -1 3 1 2 4 -3
CROSSREFS
Cf. A209115.
Sequence in context: A182118 A111387 A067129 * A238087 A063079 A362786
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 05 2012
STATUS
approved