Number of permutations of [n] avoiding {3412, 1324, 2341}.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =21a(5) =73a(6) =238a(7) =721a(8) =2046a(9) =5501a(10) =14158a(11) =35172a(12) =84895a(13) =200133a(14) =462714a(15) =1052727a(16) =2363200a(17) =5245849a(18) =11535354a(19) =25163458a(20) =54518249a(21) =117424881a(22) =251631318a(23) =536828413a(24) =1140787234a(25) =2415828037a(26) =5100146838a(27) =10737245792a(28) =22548348403a(29) =47244338829