Number of order-preserving or order-reversing full contraction mappings of an n-chain.

Terms

a(0) =1a(1) =4a(2) =13a(3) =36a(4) =91a(5) =218a(6) =505a(7) =1144a(8) =2551a(9) =5622a(10) =12277a(11) =26612a(12) =57331a(13) =122866a(14) =262129a(15) =557040a(16) =1179631a(17) =2490350a(18) =5242861a(19) =11010028a(20) =23068651a(21) =48234474a(22) =100663273a(23) =209715176a(24) =436207591a(25) =905969638a(26) =1879048165a(27) =3892314084a(28) =8053063651a(29) =16642998242