a(n) is the number of complement pairs of 2n-bead balanced bicolor necklaces.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =11a(6) =36a(7) =118a(8) =395a(9) =1337a(10) =4598a(11) =15986a(12) =56270a(13) =199854a(14) =716132a(15) =2584754a(16) =9391051a(17) =34315811a(18) =126040590a(19) =465062362a(20) =1723070794a(21) =6407806952a(22) =23910175804a(23) =89493721076a(24) =335912391966