A208997 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.

5, 51, 253, 874, 2354, 5404, 11010, 20553, 35781, 58971, 92851, 140818, 206798, 295528, 412352, 563577, 756175, 998245, 1298615, 1667392, 2115476, 2655216, 3299792, 4064019, 4963585, 6015983, 7239629, 8654930, 10283232, 12148080

Offset

1,1

Comments

Row 6 of A208993.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).

Example

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

Crossrefs

Sequence in context: A064019 A134938 A068540 * A041043 A362516 A369295

Adjacent sequences: A208994 A208995 A208996 * A208998 A208999 A209000

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved