A209347 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

14, 146, 770, 2698, 7358, 16968, 34720, 64942, 113288, 186906, 294616, 447084, 657006, 939270, 1311146, 1792454, 2405742, 3176460, 4133144, 5307578, 6734984, 8454190, 10507808, 12942408, 15808702, 19161706, 23060930, 27570546, 32759566

Offset

1,1

Comments

Row 6 of A209344.

Links

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

Formula

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

Empirical g.f.: 2*x*(7 + 45*x + 128*x^2 + 167*x^3 + 128*x^4 + 48*x^5 + 5*x^6) / ((1 - x)^6*(1 + x)*(1 + x + x^2)). - Colin Barker, Jul 09 2018

Example

Some solutions for n=8:
  -5  -8  -6  -2  -4  -6  -6  -3  -3  -8  -8  -6  -5  -4  -5  -8
  -4   1  -1  -2  -1  -5  -3  -1  -1   0  -3  -1   1  -2   2  -7
  -2  -2   4   0   5  -2   5   1   2  -4   7   1  -2   1   4   8
   4   3  -4   0  -4   2   5   2  -3  -2   3   3  -3   2   0   6
   7   1  -1   1   4   3  -5  -3   1   7  -7  -3   7   3  -4   3
   0   5   8   3   0   8   4   4   4   7   8   6   2   0   3  -2

Crossrefs

Cf. A209344.

Sequence in context: A099914 A016278 A241169 * A132934 A027473 A002451

Adjacent sequences: A209344 A209345 A209346 * A209348 A209349 A209350

Keyword

nonn

Author

R. H. Hardin, Mar 06 2012

Status

approved