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

Terms

a(0) =0a(1) =2a(2) =5a(3) =16a(4) =45a(5) =132a(6) =385a(7) =1136a(8) =3365a(9) =10012a(10) =29865a(11) =89256a(12) =267085a(13) =799892a(14) =2396945a(15) =7185376a(16) =21545205a(17) =64613772a(18) =193797625a(19) =581305496a(20) =1743741725a(21) =5230875652a(22) =15691927905a(23) =47074385616a(24) =141220360645a(25) =423655489532