a(n) = Sum_{k=0..floor(n/3)} binomial(n-3*k,floor(k/3)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =2a(6) =3a(7) =3a(8) =3a(9) =3a(10) =4a(11) =5a(12) =6a(13) =8a(14) =10a(15) =12a(16) =15a(17) =18a(18) =21a(19) =24a(20) =28a(21) =33a(22) =39a(23) =47a(24) =57a(25) =69a(26) =84a(27) =102a(28) =123a(29) =147