A209119 Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

25, 865, 7377, 35253, 121117, 336055, 802125, 1712987, 3357255, 6145113, 10639105, 17587647, 27961449, 42994779, 64228807, 93558167, 133282385, 186159325, 255461573, 345038397, 459378989, 603678961, 783912475, 1006905635, 1280412799

Offset

1,1

Comments

Row 7 of A209115.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 7*a(n-2) + 9*a(n-3) - 11*a(n-4) + 12*a(n-5) - 12*a(n-6) + 10*a(n-7) - 6*a(n-8) + 3*a(n-9) - 3*a(n-11) + 6*a(n-12) - 10*a(n-13) + 12*a(n-14) - 12*a(n-15) + 11*a(n-16) - 9*a(n-17) + 7*a(n-18) - 4*a(n-19) + a(n-20) for n > 22.

Example

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

Crossrefs

Sequence in context: A181892 A274469 A223258 * A350983 A224478 A159332

Adjacent sequences: A209116 A209117 A209118 * A209120 A209121 A209122

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved