A208947 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.

8, 68, 274, 766, 1722, 3376, 6004, 9928, 15514, 23178, 33378, 46624, 63464, 84496, 110366, 141766, 179426, 224132, 276712, 338040, 409034, 490662, 583934, 689912, 809696, 944436, 1095330, 1263622, 1450594, 1657584, 1885972, 2137184, 2412690

Offset

1,1

Comments

Row 5 of A208945.

Links

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

Formula

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

Empirical g.f.: 2*x*(4 + 22*x + 47*x^2 + 66*x^3 + 63*x^4 + 48*x^5 + 21*x^6 + 6*x^7 - x^8) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 07 2018

Example

Some solutions for n=5:
  -5  -3  -4  -4  -5  -5  -5  -5  -3  -4  -5  -5  -4  -5  -2  -4
   0   2   2   2  -5   4   5  -5   1  -2   4   3   1  -3   4   0
   5  -2   3  -2   3  -2  -1   3  -2   2   2   3   3   2  -1   5
  -2   4   2   5   5   2  -4   2   5   5   1   0  -2   1   0   1
   2  -1  -3  -1   2   1   5   5  -1  -1  -2  -1   2   5  -1  -2

Crossrefs

Cf. A208945.

Sequence in context: A250258 A192091 A050841 * A296670 A263477 A249390

Adjacent sequences: A208944 A208945 A208946 * A208948 A208949 A208950

Keyword

nonn

Author

R. H. Hardin, Mar 03 2012

Status

approved