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

Terms

a(0) =1a(1) =0a(2) =3a(3) =6a(4) =6a(5) =30a(6) =25a(7) =90a(8) =120a(9) =238a(10) =441a(11) =672a(12) =1333a(13) =2016a(14) =3681a(15) =5946a(16) =9945a(17) =16698a(18) =26876a(19) =45012a(20) =72216a(21) =118524a(22) =191178a(23) =308346a(24) =497559a(25) =795318a(26) =1276752a(27) =2033294a(28) =3242088a(29) =5150502