A209009 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.

1, 5, 13, 31, 71, 137, 243, 399, 619, 927, 1329, 1857, 2525, 3355, 4385, 5627, 7121, 8893, 10971, 13407, 16213, 19449, 23143, 27333, 32083, 37413, 43389, 50053, 57447, 65651, 74683, 84631, 95537, 107455, 120475, 134625, 149997, 166649, 184637

Offset

1,2

Comments

Row 5 of A209007.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19).

Example

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

Crossrefs

Sequence in context: A335307 A067333 A369176 * A118646 A097969 A082280

Adjacent sequences: A209006 A209007 A209008 * A209010 A209011 A209012

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved