We discuss an enumerative technique called generating trees which was introduced in the study of Baxter permutations. We apply the technique to some other classes of permutations with forbidden subsequences. We rederive some known results, e.g. |Sn(132, 231)| = 2n and |Sn(123, 132, 213)| = Fn, and add several new ones: Sn(123, 3241), Sn(123, 3214), Sn(123, 2143). Finally, we argue for the broader use of generating trees in combinatorial enumeration.
West, J. (1996). Generating trees and forbidden subsequences. Discrete Mathematics, 157(1–3), 363–374. https://doi.org/10.1016/S0012-365X(96)83023-8