Number of permutations of [n] avoiding {1234, 1324, 3412}.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =21a(5) =73a(6) =236a(7) =700a(8) =1919a(9) =4927a(10) =12006a(11) =28090a(12) =63705a(13) =141109a(14) =307088a(15) =659576a(16) =1402947a(17) =2962699a(18) =6223018a(19) =13018294a(20) =27148925a(21) =56478465a(22) =117258996a(23) =243044020a(24) =503038535a(25) =1039847767a(26) =2147071790a(27) =4428689074a(28) =9126212193a(29) =18789776461