a(n) = ceiling(e^(n/3)).

Terms

a(0) =2a(1) =2a(2) =3a(3) =4a(4) =6a(5) =8a(6) =11a(7) =15a(8) =21a(9) =29a(10) =40a(11) =55a(12) =77a(13) =107a(14) =149a(15) =208a(16) =290a(17) =404a(18) =564a(19) =786a(20) =1097a(21) =1531a(22) =2136a(23) =2981a(24) =4161a(25) =5807a(26) =8104a(27) =11309a(28) =15783a(29) =22027