a(n) = Sum_{k=0..floor(2*n/3)} binomial(2*k+1,2*n-3*k).

Terms

a(0) =1a(1) =0a(2) =3a(3) =2a(4) =10a(5) =12a(6) =36a(7) =57a(8) =138a(9) =250a(10) =549a(11) =1060a(12) =2227a(13) =4427a(14) =9120a(15) =18364a(16) =37513a(17) =75949a(18) =154603a(19) =313701a(20) =637699a(21) =1295022a(22) =2631240a(23) =5344988a(24) =10858285a(25) =22058847a(26) =44810670a(27) =91034937a(28) =184929945a(29) =375691009