A208828 Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.

32, 609, 4390, 19657, 65134, 177097, 417204, 883409, 1720628, 3135633, 5410378, 8921049, 14153874, 21728505, 32416136, 47167393, 67132584, 93694273, 128489486, 173447145, 230812054, 303187369, 393560188, 505349233, 642431868, 809197169

Offset

1,1

Comments

Row 7 of A208825.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 8*a(n-3) + 14*a(n-4) - 14*a(n-6) + 8*a(n-7) + 3*a(n-8) - 4*a(n-9) + a(n-10).

Empirical g.f.: x*(32 + 481*x + 2050*x^2 + 4180*x^3 + 4100*x^4 + 2126*x^5 + 462*x^6 + 28*x^7 - 4*x^8 + x^9) / ((1 - x)^7*(1 + x)^3). - Colin Barker, Jul 07 2018

Example

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

Crossrefs

Cf. A208825.

Sequence in context: A332262 A088914 A036903 * A013699 A283279 A004337

Adjacent sequences: A208825 A208826 A208827 * A208829 A208830 A208831

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved