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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =6a(5) =13a(6) =22a(7) =33a(8) =91a(9) =226a(10) =474a(11) =877a(12) =1938a(13) =4586a(14) =10326a(15) =21409a(16) =45867a(17) =103423a(18) =234271a(19) =511426a(20) =1110544a(21) =2460822a(22) =5526188a(23) =12282861a(24) =27073156a(25) =59942598a(26) =133861825a(27) =298874122a(28) =664509858a(29) =1476912298