A045680 Number of 2n-bead balanced binary necklaces of fundamental period 2n equivalent to reverse.

1, 1, 1, 1, 4, 5, 17, 19, 64, 68, 245, 251, 900, 923, 3411, 3425, 12800, 12869, 48532, 48619, 184500, 184735, 705179, 705431, 2703168, 2704150, 10399675, 10400530, 40113164, 40116599, 155113825, 155117519, 601067520, 601080137, 2333593349