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

Terms

a(0) =1a(1) =3a(2) =10a(3) =36a(4) =134a(5) =507a(6) =1937a(7) =7449a(8) =28783a(9) =111623a(10) =434130a(11) =1692387a(12) =6610292a(13) =25861384a(14) =101319095a(15) =397428091a(16) =1560588454a(17) =6133768656a(18) =24128550045a(19) =94986663925a(20) =374188128311