A208946 Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.

5, 22, 57, 122, 223, 366, 563, 820, 1143, 1544, 2029, 2604, 3281, 4066, 4965, 5990, 7147, 8442, 9887, 11488, 13251, 15188, 17305, 19608, 22109, 24814, 27729, 30866, 34231, 37830, 41675, 45772, 50127, 54752, 59653, 64836, 70313, 76090, 82173, 88574

Offset

1,1

Comments

Row 4 of A208945.

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 + 6*x^2 + 7*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Mar 07 2018

Example

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

Crossrefs

Cf. A208945.

Sequence in context: A209116 A301499 A033445 * A245301 A256971 A273685

Adjacent sequences: A208943 A208944 A208945 * A208947 A208948 A208949

Keyword

nonn

Author

R. H. Hardin, Mar 03 2012

Status

approved