a(n) = Sum_{k=0..floor(n/3)} binomial(k+2,3*n-9*k+2).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =0a(5) =0a(6) =6a(7) =0a(8) =0a(9) =10a(10) =1a(11) =0a(12) =15a(13) =6a(14) =0a(15) =21a(16) =21a(17) =0a(18) =28a(19) =56a(20) =1a(21) =36a(22) =126a(23) =9a(24) =45a(25) =252a(26) =45a(27) =55a(28) =462a(29) =165