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A209118
Number of 6-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
15, 238, 1373, 5032, 14037, 32802, 67681, 127310, 222965, 368920, 582789, 885874, 1303543, 1865552, 2606403, 3565722, 4788571, 6325826, 8234535, 10578240, 13427355, 16859514, 20959913, 25821668, 31546173, 38243442, 46032457, 55041546
OFFSET
1,1
COMMENTS
Row 6 of A209115.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 7*a(n-5) - 8*a(n-6) + 7*a(n-7) - 5*a(n-8) + 5*a(n-9) - 6*a(n-10) + 4*a(n-11) - a(n-12) for n > 13.
Empirical g.f.: x*(15 + 178*x + 511*x^2 + 893*x^3 + 1032*x^4 + 1066*x^5 + 854*x^6 + 561*x^7 + 155*x^8 + 26*x^9 - 23*x^10 + 16*x^11 - 4*x^12) / ((1 - x)^6*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jul 08 2018
EXAMPLE
Some solutions for n=6:
-6 -4 -6 -5 -5 -6 -4 -5 -6 -5 -5 -3 -6 -5 -6 -6
1 0 -1 4 -2 0 3 3 2 -4 -4 -3 4 -2 -5 3
5 -2 -5 -5 -1 2 -2 -5 -3 5 2 2 2 0 2 3
-3 -2 2 4 3 -2 0 4 6 -3 0 -2 -2 0 6 -1
2 5 5 -2 -1 2 0 1 1 2 5 5 -1 6 5 5
1 3 5 4 6 4 3 2 0 5 2 1 3 1 -2 -4
CROSSREFS
Cf. A209115.
Sequence in context: A097582 A351527 A057007 * A093745 A071811 A157456
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 05 2012
STATUS
approved