A208827 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.

18, 167, 828, 2821, 7582, 17339, 35288, 65769, 114442, 188463, 296660, 449709, 660310, 943363, 1316144, 1798481, 2412930, 3184951, 4143084, 5319125, 6748302, 8469451, 10525192, 12962105, 15830906, 19186623, 23088772, 27601533, 32793926

Offset

1,1

Comments

Row 6 of A208825.

Links

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

Formula

Empirical: a(n) = (22/15)*n^5 + (11/3)*n^4 + (14/3)*n^3 + (13/3)*n^2 + (43/15)*n + 1.

Conjectures from Colin Barker, Jul 07 2018: (Start)

G.f.: x*(18 + 59*x + 96*x^2 - 2*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A208825.

Sequence in context: A099196 A041618 A055915 * A327792 A071539 A125381

Adjacent sequences: A208824 A208825 A208826 * A208828 A208829 A208830

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved