Largest order of a rooted tree that does not contain a rooted caterpillar subtree of order n.

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =5a(5) =7a(6) =11a(7) =16a(8) =23a(9) =34a(10) =49a(11) =70a(12) =103a(13) =148a(14) =211a(15) =310a(16) =445a(17) =634a(18) =931a(19) =1336a(20) =1903a(21) =2794a(22) =4009a(23) =5710a(24) =8383a(25) =12028a(26) =17131a(27) =25150a(28) =36085a(29) =51394