The study investigates whether large‑language‑model coding agents can automate generalized task‑and‑motion planning (TAMP) by synthesizing programs that transfer across problem instances. Using a fixed synthesis budget, each agent receives a natural‑language task description and simulator access, interacts with the environment to gather data, and writes a program that is later frozen and evaluated on unseen scenarios. The authors test three configurations—Claude Code (Opus 5) and two Codex variants (GPT‑5.6 Sol and GPT‑6 Astra)—on 28 simulated environments drawn from KinDER and PDDLStream, extending the original benchmarks to higher object counts. For each configuration they generate 980 candidate programs, which are each run on 100 held‑out instances, yielding 98 000 total evaluation episodes. Across all environments where a hand‑engineered planner is available (16 tasks), the agents achieve mean success rates ranging from 56 % to 95 %, substantially exceeding the planner’s 47 % baseline as well as one‑shot generation and an LLM‑based generalized planning approach. Notably, as the number of objects increases, the agents’ programs retain higher success while consuming roughly an order of magnitude less computation per instance on average. Interaction logs reveal that the agents calibrate physical models, probe edge cases, and iteratively refine strategies during synthesis. The authors release the full code and prompts, positioning coding agents as a strong baseline for generalized TAMP.