a(n) = Sum_{k=1..n} C(3*k,k)/3.

Terms

a(0) =1a(1) =6a(2) =34a(3) =199a(4) =1200a(5) =7388a(6) =46148a(7) =291305a(8) =1853580a(9) =11868585a(10) =76380825a(11) =493606725a(12) =3201081873a(13) =20821158233a(14) =135776966761a(15) =887393271310