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

Terms

a(0) =1a(1) =2a(2) =7a(3) =35a(4) =200a(5) =1201a(6) =7389a(7) =46149a(8) =291306a(9) =1853581a(10) =11868586a(11) =76380826a(12) =493606726a(13) =3201081874a(14) =20821158234a(15) =135776966762a(16) =887393271311