a(n) = binomial(n, floor(n/3)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =4a(5) =5a(6) =15a(7) =21a(8) =28a(9) =84a(10) =120a(11) =165a(12) =495a(13) =715a(14) =1001a(15) =3003a(16) =4368a(17) =6188a(18) =18564a(19) =27132a(20) =38760a(21) =116280a(22) =170544a(23) =245157a(24) =735471a(25) =1081575a(26) =1562275a(27) =4686825a(28) =6906900a(29) =10015005