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

1,1

Comments

Row 5 of A208825.

Links

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

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)

Example

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

Crossrefs

Cf. A208825.

Sequence in context: A153492 A107125 A212105 * A206808 A197369 A059937

Adjacent sequences: A208823 A208824 A208825 * A208827 A208828 A208829

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved