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

Terms

a(0) =1a(1) =4a(2) =20a(3) =111a(4) =650a(5) =3927a(6) =24207a(7) =151316a(8) =955604a(9) =6082374a(10) =38954135a(11) =250730636a(12) =1620527481a(13) =10510253485a(14) =68368227668a(15) =445864207407