Number of permutations of [n] avoiding {1243, 2314, 3412}.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =21a(5) =73a(6) =238a(7) =722a(8) =2054a(9) =5541a(10) =14323a(11) =35788a(12) =87043a(13) =207201a(14) =484772a(15) =1118334a(16) =2550164a(17) =5759101a(18) =12899521a(19) =28689880a(20) =63419177a(21) =139435017a(22) =305102778a(23) =664755562a(24) =1442788402a(25) =3120497429a(26) =6727583999a(27) =14461863108a(28) =31004177695a(29) =66303416497