A209075 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.

19, 265, 1465, 5239, 14431, 33469, 68723, 128845, 225127, 371859, 586669, 890881, 1309873, 1873417, 2616037, 3577367, 4802491, 6342301, 8253855, 10600717, 13453315, 16889299, 20993881, 25860193, 31589645, 38292265, 46087057, 55102359

Offset

1,1

Comments

Row 6 of A209073.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8) for n > 9.

Empirical g.f.: x*(19 + 170*x + 330*x^2 + 355*x^3 + 161*x^4 + 30*x^5 - 16*x^6 + 9*x^7 - 2*x^8) / ((1 - x)^6*(1 + x + x^2)). - Colin Barker, Jul 08 2018

Example

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

Crossrefs

Cf. A209073.

Sequence in context: A294828 A016257 A021104 * A017161 A036736 A016254

Adjacent sequences: A209072 A209073 A209074 * A209076 A209077 A209078

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved