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

Terms

a(0) =0a(1) =1a(2) =2a(3) =5a(4) =9a(5) =18a(6) =36a(7) =70a(8) =138a(9) =273a(10) =539a(11) =1068a(12) =2120a(13) =4212a(14) =8380a(15) =16689a(16) =33261a(17) =66334a(18) =132364a(19) =264234a(20) =527670a(21) =1054049a(22) =2106007a(23) =4208632a(24) =8411792a(25) =16814728a(26) =33615128a(27) =67207073a(28) =134376633a(29) =268692570