G.f.: (1-x+sqrt(1-2*x-3*x^2))/(1-3*x+x^2+x^3+(1-x^2)*sqrt(1-2*x-3*x^2)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =22a(6) =56a(7) =147a(8) =393a(9) =1065a(10) =2915a(11) =8042a(12) =22330a(13) =62339a(14) =174837a(15) =492313a(16) =1391134a(17) =3943130a(18) =11207594a(19) =31934552a(20) =91197474a(21) =260969372a(22) =748176873a(23) =2148622932a(24) =6180146228a(25) =17801978083a(26) =51347929943a(27) =148293450023a(28) =428774359142