A208948 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.

20, 264, 1464, 5238, 14430, 33468, 68722, 128844, 225126, 371858, 586668, 890880, 1309872, 1873416, 2616036, 3577366, 4802490, 6342300, 8253854, 10600716, 13453314, 16889298, 20993880, 25860192, 31589644, 38292264, 46087056, 55102358

Offset

1,1

Comments

Row 6 of A208945.

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).

Empirical g.f.: 2*x*(10 + 82*x + 172*x^2 + 169*x^3 + 88*x^4 + 7*x^5) / ((1 - x)^6*(1 + x + x^2)). - Colin Barker, Jul 07 2018

Example

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

Crossrefs

Cf. A208945.

Sequence in context: A022111 A025943 A025961 * A278408 A229562 A021854

Adjacent sequences: A208945 A208946 A208947 * A208949 A208950 A208951

Keyword

nonn

Author

R. H. Hardin, Mar 03 2012

Status

approved