Number of bipartite partitions of ceiling(n/2) white objects and floor(n/2) black ones.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =16a(6) =31a(7) =57a(8) =109a(9) =189a(10) =339a(11) =589a(12) =1043a(13) =1752a(14) =2998a(15) =4987a(16) =8406a(17) =13715a(18) =22652a(19) =36535a(20) =59521a(21) =94664a(22) =151958a(23) =239241a(24) =379693a(25) =591271a(26) =927622a(27) =1431608a(28) =2224235a(29) =3402259