A208826 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.

7, 45, 155, 415, 905, 1755, 3085, 5077, 7891, 11761, 16887, 23555, 32005, 42575, 55545, 71305, 90175, 112597, 138931, 169671, 205217, 246115, 292805, 345885, 405835, 473305, 548815, 633067, 726621, 830231, 944497, 1070225, 1208055

Offset: 1

Author

R. H. Hardin, Mar 01 2012

Keywords

• nonn

Comments

Row 5 of A208825.

Examples

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

Links

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

Crossrefs

Cf. A208825.

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).

Conjectures from Colin Barker, Jul 06 2018: (Start)

G.f.: x*(7 + 24*x + 27*x^2 + 30*x^3 + 5*x^4 - 2*x^5 + x^6) / ((1 - x)^5*(1 + x)^2).

a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 44*n + 24) / 24 for n even.

a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 26*n + 15) / 24 for n odd.

(End)