a(n) = Sum_{k=0..floor(n/2)} binomial(3*k,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =3a(4) =1a(5) =15a(6) =16a(7) =37a(8) =127a(9) =150a(10) =505a(11) =1029a(12) =1861a(13) =5224a(14) =9497a(15) =21777a(16) =50199a(17) =98313a(18) =232681a(19) =490723a(20) =1047105a(21) =2373982a(22) =4971986a(23) =10993174a(24) =24013198a(25) =51346109a(26) =113484808a(27) =244619349a(28) =531470618a(29) =1162833495