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

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =0a(6) =1a(7) =1a(8) =1a(9) =4a(10) =1a(11) =10a(12) =1a(13) =20a(14) =2a(15) =35a(16) =8a(17) =56a(18) =29a(19) =84a(20) =85a(21) =121a(22) =211a(23) =175a(24) =463a(25) =275a(26) =925a(27) =506a(28) =1718a(29) =1079