Upper (1/3,1/2)-midsequence of ((2^n)) and ((3^n)); see Comments.

Terms

a(0) =1a(1) =3a(2) =6a(3) =17a(4) =46a(5) =133a(6) =386a(7) =1137a(8) =3366a(9) =10013a(10) =29866a(11) =89257a(12) =267086a(13) =799893a(14) =2396946a(15) =7185377a(16) =21545206a(17) =64613773a(18) =193797626a(19) =581305497a(20) =1743741726a(21) =5230875653a(22) =15691927906a(23) =47074385617a(24) =141220360646a(25) =423655489533