Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 321.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =12a(6) =29a(7) =72a(8) =182a(9) =466a(10) =1207a(11) =3158a(12) =8334a(13) =22158a(14) =59299a(15) =159614a(16) =431838a(17) =1173710a(18) =3203244a(19) =8774780a(20) =24118522a(21) =66497316a(22) =183858411a(23) =509670494a(24) =1416231616a(25) =3944027402a(26) =11006186760a(27) =30772507128a(28) =86191006746a(29) =241815195292