A208601 Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.

57, 1163, 8671, 39019, 129823, 353333, 833253, 1764925, 3438877, 6267735, 10816499, 17836183, 28300819, 43447825, 64821737, 94321305, 134249953, 187369603, 256957863, 346868579, 461595751, 606340813, 787083277, 1010654741

Offset: 1

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn

Comments

Row 7 of A208597.

Examples

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

Links

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

Crossrefs

Cf. A208597.

Formula

Empirical: a(n) = (841/180)*n^6 + (841/60)*n^5 + (325/18)*n^4 + (51/4)*n^3 + (949/180)*n^2 + (37/30)*n + 1.

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

G.f.: x*(57 + 764*x + 1727*x^2 + 750*x^3 + 71*x^4 - 6*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)