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

Terms

a(0) =2a(1) =3a(2) =5a(3) =11a(4) =17a(5) =41a(6) =65a(7) =155a(8) =257a(9) =593a(10) =1025a(11) =2291a(12) =4097a(13) =8921a(14) =16385a(15) =34955a(16) =65537a(17) =137633a(18) =262145a(19) =543971a(20) =1048577a(21) =2156201a(22) =4194305a(23) =8565755a(24) =16777217a(25) =34085873a(26) =67108865a(27) =135812051a(28) =268435457a(29) =541653881