Upper (1/2)-midsequence of (2^n) and F(n), where F = A000045 (Fibonacci numbers); see Comments.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =10a(5) =19a(6) =36a(7) =71a(8) =139a(9) =273a(10) =540a(11) =1069a(12) =2120a(13) =4213a(14) =8381a(15) =16689a(16) =33262a(17) =66335a(18) =132364a(19) =264235a(20) =527671a(21) =1054049a(22) =2106008a(23) =4208633a(24) =8411792a(25) =16814729a(26) =33615129a(27) =67207073a(28) =134376634a(29) =268692571