A208598 Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.

6, 23, 60, 125, 226, 371, 568, 825, 1150, 1551, 2036, 2613, 3290, 4075, 4976, 6001, 7158, 8455, 9900, 11501, 13266, 15203, 17320, 19625, 22126, 24831, 27748, 30885, 34250, 37851, 41696, 45793, 50150, 54775, 59676, 64861, 70338, 76115, 82200, 88601

Offset

1,1

Comments

Row 4 of A208597.

Links

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

Formula

Empirical: a(n) = (4/3)*n^3 + 2*n^2 + (5/3)*n + 1.

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

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

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

(End)

Example

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

Crossrefs

Cf. A208597.

Sequence in context: A273214 A273276 A273252 * A327794 A119712 A273314

Adjacent sequences: A208595 A208596 A208597 * A208599 A208600 A208601

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved