A208600 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.

26, 297, 1564, 5457, 14838, 34153, 69784, 130401, 227314, 374825, 590580, 895921, 1316238, 1881321, 2625712, 3589057, 4816458, 6358825, 8273228, 10623249, 13479334, 16919145, 21027912, 25898785, 31633186, 38341161, 46141732, 55163249

Offset

1,1

Comments

Row 6 of A208597.

Links

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

Formula

Empirical: a(n) = (44/15)*n^5 + (22/3)*n^4 + (23/3)*n^3 + (14/3)*n^2 + (12/5)*n + 1.

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

G.f.: x*(26 + 141*x + 172*x^2 + 8*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=4:
  -4  -4  -4  -3  -4  -2  -4  -4  -4  -4  -3  -4  -4  -3  -3  -1
   4   3   2   2  -3  -2  -1   2   0  -1   3   4   2  -1   3   0
   0   2  -1   3  -2   2   0  -3   4   2  -3  -2   1   2   0  -1
   1   1  -3   0   3   0  -1   0  -1   1   3   0   3  -2  -2   0
  -1   1   3   0   4  -2   4   3   4   4  -3   1  -2   4   0  -1
   0  -3   3  -2   2   4   2   2  -3  -2   3   1   0   0   2   3

Crossrefs

Sequence in context: A020925 A224331 A125414 * A010831 A022718 A014472

Adjacent sequences: A208597 A208598 A208599 * A208601 A208602 A208603

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved