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.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A209115 A209116 A209117 * A209119 A209120 A209121

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved