36864

1) Eight beads - 6 (I drew a symmetry line and then distributed the beads. I drew every combination.)
2) Nine beads - 6
3) Ten beads - 0
4) Eleven beads - 8
5) Twelve beads - 10
6) Thirteen beads - 10

If there are an odd number of each color of beads, there are no combinations. If there are an even number of each color, then the number of combinations is two less than the total number of beads. If there is an even number of one color and an odd number of the other color, then the number of combinations is three less than the total number of beads.