A209074 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.

8, 70, 276, 766, 1722, 3378, 6006, 9928, 15514, 23180, 33380, 46624, 63464, 84498, 110368, 141766, 179426, 224134, 276714, 338040, 409034, 490664, 583936, 689912, 809696, 944438, 1095332, 1263622, 1450594, 1657586, 1885974, 2137184, 2412690

Offset

1,1

Comments

Row 5 of A209073.

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 + 23*x + 45*x^2 + 66*x^3 + 64*x^4 + 49*x^5 + 21*x^6 + 4*x^7) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 08 2018

Example

Some solutions for n=6:
  -6  -3  -6  -3  -4  -4  -6  -2  -3  -3  -5  -4  -6  -3  -4  -3
   3   0   5  -1   5  -1   6  -2   1   5  -4   5   3  -1   1   1
   3  -1   0  -3  -1   6   2   0   2  -2   6   4   6   2   6   0
   4   0  -3   3   0   0  -3   2   1   0   6  -3  -2   4  -2  -1
  -4   4   4   4   0  -1   1   2  -1   0  -3  -2  -1  -2  -1   3

Crossrefs

Cf. A209073.

Sequence in context: A336951 A335114 A226597 * A124152 A293069 A056631

Adjacent sequences: A209071 A209072 A209073 * A209075 A209076 A209077

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved