a(n) = ceiling((2^n + 1 - 2*floor(2^(n/2)))/2).

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =12a(5) =25a(6) =54a(7) =113a(8) =235a(9) =481a(10) =980a(11) =1985a(12) =4007a(13) =8065a(14) =16204a(15) =32513a(16) =65175a(17) =130561a(18) =261421a(19) =523265a(20) =1047129a(21) =2095105a(22) =4191409a(23) =8384513a(24) =16771425a(25) =33546241a(26) =67097280a(27) =134201345a(28) =268412287a(29) =536838145