a(n) = Sum_{k=0..floor(n/3)} binomial(k+1,3*n-9*k+1).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =0a(5) =0a(6) =3a(7) =0a(8) =0a(9) =4a(10) =1a(11) =0a(12) =5a(13) =5a(14) =0a(15) =6a(16) =15a(17) =0a(18) =7a(19) =35a(20) =1a(21) =8a(22) =70a(23) =8a(24) =9a(25) =126a(26) =36a(27) =10a(28) =210a(29) =120