a(n) = (2^n + 2^[ n/2 ] )/2.

Terms

a(0) =3a(1) =5a(2) =10a(3) =18a(4) =36a(5) =68a(6) =136a(7) =264a(8) =528a(9) =1040a(10) =2080a(11) =4128a(12) =8256a(13) =16448a(14) =32896a(15) =65664a(16) =131328a(17) =262400a(18) =524800a(19) =1049088a(20) =2098176a(21) =4195328a(22) =8390656a(23) =16779264a(24) =33558528a(25) =67112960a(26) =134225920a(27) =268443648