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

1,1

Comments

Row 7 of A208597.

Links

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

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)

Example

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

Crossrefs

Cf. A208597.

Sequence in context: A116181 A336734 A333109 * A000505 A332911 A179466

Adjacent sequences: A208598 A208599 A208600 * A208602 A208603 A208604

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved