AI 中文总结
该研究基于Zeilberger的计算框架，复现L-四格骨牌铺砌的生成函数，还得到宽度5-9的显式生成函数及OEIS未收录的新序列，拓展了多联骨牌铺砌的枚举研究。
AI 中文摘要
我们重新审视Zeilberger的多联骨牌铺砌枚举计算框架，展示其用于计数k×n棋盘被L-四格骨牌（允许旋转）铺砌的应用。近期Bělohoubek和Slavík给出了2n×4棋盘被L-四格骨牌铺砌的生成函数，受其工作启发，我们先通过自动复现该生成函数验证方法，再将方法应用于宽度5至9的情况，得到显式有理生成函数及未收录于OEIS的新整数序列。
英文摘要
We revisit Zeilberger's computational framework for enumerating polyomino tilings and demonstrate its use in counting tilings of $k\times n$ boards by $L$-tetrominoes, allowing rotations. Recently, Bělohoubek and Slavík gave a generating function for tilings of $2n\times 4$ boards by $L$-tetrominoes. Motivated by their work, we first verify the method by automatically recovering their generating function. We then apply the method to widths $5$ through $9$ and obtain explicit rational generating functions and new integer sequences that are not currently listed in the OEIS.
Comments10 pages, 6 figures, 3 tables. (V2) Correcting some typos
