a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k)*binomial(4*k,k)/(3*k+1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =25a(7) =64a(8) =169a(9) =443a(10) =1181a(11) =3224a(12) =8897a(13) =24701a(14) =69161a(15) =195255a(16) =554577a(17) =1583109a(18) =4541461a(19) =13086574a(20) =37856437a(21) =109892403a(22) =320034309a(23) =934774902a(24) =2737689189a(25) =8037746691a(26) =23652564261a(27) =69749727716a(28) =206091735797a(29) =610061655665