a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/3).

Terms

a(0) =2a(1) =3a(2) =4a(3) =5a(4) =7a(5) =9a(6) =12a(7) =16a(8) =21a(9) =28a(10) =38a(11) =50a(12) =67a(13) =89a(14) =119a(15) =159a(16) =212a(17) =282a(18) =376a(19) =502a(20) =669a(21) =892a(22) =1189a(23) =1586a(24) =2114a(25) =2819a(26) =3759a(27) =5012a(28) =6682a(29) =8910