Number of different, not necessarily connected, unlabeled trivalent diagrams of size n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =7a(5) =10a(6) =24a(7) =37a(8) =63a(9) =112a(10) =200a(11) =318a(12) =607a(13) =1058a(14) =1814a(15) =3247a(16) =6004a(17) =10316a(18) =19048a(19) =35478a(20) =63496a(21) =117023a(22) =223822a(23) =408121a(24) =766661a(25) =1484363a(26) =2775201a(27) =5270079a(28) =10357605a(29) =19714259