Generalized (3,-1) Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =5a(6) =11a(7) =21a(8) =38a(9) =71a(10) =141a(11) =289a(12) =591a(13) =1195a(14) =2410a(15) =4897a(16) =10051a(17) =20763a(18) =42996a(19) =89139a(20) =185170a(21) =385809a(22) =806349a(23) =1689573a(24) =3547152a(25) =7459715a(26) =15714655a(27) =33161821a(28) =70095642a(29) =148388521