a(1) = 1 and a(n) = ceiling((Sum_{k=1..n-1} a(k))/3) for n >= 2.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =3a(7) =4a(8) =5a(9) =7a(10) =9a(11) =12a(12) =16a(13) =22a(14) =29a(15) =39a(16) =52a(17) =69a(18) =92a(19) =123a(20) =164a(21) =218a(22) =291a(23) =388a(24) =517a(25) =690a(26) =920a(27) =1226a(28) =1635a(29) =2180