Number of permutations in S_n avoiding the strings 123, 321 and 231.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =11a(6) =23a(7) =63a(8) =153a(9) =489a(10) =1329a(11) =4785a(12) =14235a(13) =56475a(14) =181215a(15) =780255a(16) =2672145a(17) =12348945a(18) =44781345a(19) =220253985a(20) =840523635a(21) =4370620275a(22) =17465201775a(23) =95498916975a(24) =397983749625