a(n) = Sum_{k=0..floor(2*n/9)} binomial(2*n-6*k,3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =5a(6) =21a(7) =57a(8) =121a(9) =222a(10) =393a(11) =771a(12) =1741a(13) =4144a(14) =9559a(15) =20809a(16) =43363a(17) =89330a(18) =187278a(19) =403242a(20) =881965a(21) =1926984a(22) =4165149a(23) =8908347a(24) =18971395a(25) =40495930a(26) =86897116a(27) =187207093a(28) =403609483a(29) =868631315