A045630 Number of 2n-bead black-white complementable strings with n black beads and fundamental period 2n.

1, 1, 2, 9, 32, 125, 450, 1715, 6400, 24300, 92250, 352715, 1351584, 5200299, 20056582, 77558625, 300533760, 1166803109, 4537542888, 17672631899, 68923172000, 269128935495, 1052049129142, 4116715363799, 16123800483072