a(n) is the number of permutations pi of [n] that avoid {231,321} so that pi^4 avoids 132.

Terms

a(0) =0a(1) =1a(2) =2a(3) =4a(4) =7a(5) =13a(6) =23a(7) =41a(8) =72a(9) =127a(10) =223a(11) =392a(12) =688a(13) =1208a(14) =2120a(15) =3721a(16) =6530a(17) =11460a(18) =20111a(19) =35293a(20) =61935a(21) =108689a(22) =190736a(23) =334719a(24) =587391a(25) =1030800a(26) =1808928a(27) =3174448a(28) =5570768a(29) =9776017