a(n) = Sum_{k=0..floor(3*n/5)} binomial(3*n-3*k,2*k).

Terms

a(0) =1a(1) =1a(2) =4a(3) =16a(4) =52a(5) =194a(6) =685a(7) =2452a(8) =8771a(9) =31327a(10) =112004a(11) =400285a(12) =1430710a(13) =5113647a(14) =18277014a(15) =65325542a(16) =233485250a(17) =834519021a(18) =2982723523a(19) =10660798289a(20) =38103641048a(21) =136189372297a(22) =486765693153