a(1)=2; a(n)=floor((13+sum(a(1) to a(n-1)))/6).

Terms

a(0) =2a(1) =2a(2) =2a(3) =3a(4) =3a(5) =4a(6) =4a(7) =5a(8) =6a(9) =7a(10) =8a(11) =9a(12) =11a(13) =13a(14) =15a(15) =17a(16) =20a(17) =24a(18) =28a(19) =32a(20) =38a(21) =44a(22) =51a(23) =60a(24) =70a(25) =81a(26) =95a(27) =111a(28) =129a(29) =151