We introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes $I_n(000,021)$, $I_n(100,021)$, $I_n(110,021)$, $I_n(102,021)$, $I_n(100,012)$, $I_n(011,201)$, $I_n(011,210)$ and $I_n(120,210)$. Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either $\{12313,12323\}$, $\{12313,12323,12333\}$, or $\{123\cdots \ell 1\}$.

我们介绍了一种基于生成树方法的算法方法，用于枚举具有各种模式回避限制的反转序列。对于一组给定的模式，我们提出了一种算法，该算法输出相应生成树的继承规则的准确描述或 ansatz。通过使用这种方法，我们确定了模式类的生成树${我}_n(000,021)$,${我}_n(100,021)$,${我}_n(110,021)$,${我}_n(102,021)$,${我}_n(100,012)$,${我}_n(011,201)$,${我}_n(011,210)$和${我}_n(120,210)$. 然后我们使用核方法，得到每一类的生成函数，并找到枚举公式。Lin 和 Yan 研究了避免长度三模式对的反转序列的 Wilf 等价分类，并表明在 78 对中有 48 个 Wilf 类。在本文中，我们解决了此类模式类的六个开放案例。此外，我们将算法扩展到受限的增长序列并将其应用于多个类。特别是，我们提出了限制增长序列的生成函数的明确公式，避免了$\{12313,12323\}$,$\{12313,12323,12333\}$， 或者$\{123\cdots \ell \mathrm{1个}\}$.