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

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn

Comments

Row 6 of A208597.

Examples

			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
		

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)