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.

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

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

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

Adjacent sequences: A209114 A209115 A209116 * A209118 A209119 A209120

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved