a(n) = 5 + floor((1 + Sum_{j=1..n-1} a(j)) / 2).

Terms

a(0) =5a(1) =8a(2) =12a(3) =18a(4) =27a(5) =40a(6) =60a(7) =90a(8) =135a(9) =203a(10) =304a(11) =456a(12) =684a(13) =1026a(14) =1539a(15) =2309a(16) =3463a(17) =5195a(18) =7792a(19) =11688a(20) =17532a(21) =26298a(22) =39447a(23) =59171a(24) =88756a(25) =133134a(26) =199701a(27) =299552a(28) =449328a(29) =673992