a(n) = 6 + floor((1 + Sum_{j=1..n-1} a(j))/3).

Terms

a(0) =6a(1) =8a(2) =11a(3) =14a(4) =19a(5) =25a(6) =34a(7) =45a(8) =60a(9) =80a(10) =107a(11) =142a(12) =190a(13) =253a(14) =337a(15) =450a(16) =600a(17) =800a(18) =1066a(19) =1422a(20) =1896a(21) =2528a(22) =3370a(23) =4494a(24) =5992a(25) =7989a(26) =10652a(27) =14203a(28) =18937a(29) =25249