A209116 Number of 4-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, 22, 55, 120, 221, 362, 559, 816, 1137, 1538, 2023, 2596, 3273, 4058, 4955, 5980, 7137, 8430, 9875, 11476, 13237, 15174, 17291, 19592, 22093, 24798, 27711, 30848, 34213, 37810, 41655, 45752, 50105, 54730, 59631, 64812, 70289, 76066, 82147, 88548

Offset

1,1

Comments

Row 4 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) - 3*a(n-4) + 3*a(n-5) - a(n-6).

Empirical g.f.: x*(5 + 7*x + 4*x^2 + 11*x^3 - 3*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Jul 08 2018

Example

Some solutions for n=6:
  -2 -4 -5 -4 -4 -6 -3 -6 -5 -6 -4 -5 -6 -5 -5 -6
   0  1  6  2 -1  4 -2  6 -5 -3  0  5  1 -5  1  6
  -1  1 -2  1  4 -3  1  3  6  3  3  1  0  5  5 -1
   3  2  1  1  1  5  4 -3  4  6  1 -1  5  5 -1  1

Crossrefs

Cf. A209115.

Sequence in context: A273075 A272824 A273677 * A301499 A033445 A208946

Adjacent sequences: A209113 A209114 A209115 * A209117 A209118 A209119

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved