a(n) = a(n-1) + a(n - 1 minus the number of terms of a(k) == n (mod 3) so far).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =7a(5) =12a(6) =17a(7) =22a(8) =34a(9) =41a(10) =53a(11) =87a(12) =109a(13) =131a(14) =184a(15) =218a(16) =252a(17) =361a(18) =414a(19) =501a(20) =632a(21) =763a(22) =894a(23) =1112a(24) =1330a(25) =1548a(26) =1909a(27) =2161a(28) =2575a(29) =3207