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

Terms

a(0) =3a(1) =4a(2) =6a(3) =8a(4) =10a(5) =14a(6) =18a(7) =24a(8) =32a(9) =43a(10) =57a(11) =76a(12) =102a(13) =136a(14) =181a(15) =241a(16) =322a(17) =429a(18) =572a(19) =763a(20) =1017a(21) =1356a(22) =1808a(23) =2411a(24) =3214a(25) =4286a(26) =5714a(27) =7619a(28) =10159a(29) =13545