Large Language Models (LLMs) inference is central to modern AI applications, dominating worldwide datacenter workloads, making it critical to predict its energy footprint. Existing approaches estimate energy consumption as a simple linear function of input and output sequence. However, by analyzing the autoregressive structure of Transformers, which implies a fundamentally non-linear relationship between input and output sequence lengths and energy consumption, we demonstrate the existence of a generation energy minima. Peak efficiency occurs with short-to-moderate inputs and medium-length outputs, while efficiency drops sharply for long inputs or very short outputs. Consequently, we propose SweetSpot, an analytical model derived from the computational and memory-access complexity of the Transformer architecture, which accurately characterizes the efficiency curve as a function of input and output lengths. To assess accuracy, we measure energy consumption using TensorRT-LLM on NVIDIA H100 GPUs across a diverse set of LLMs ranging from 1B to 9B parameters, including OPT, LLaMA, Gemma, Falcon, Qwen2, and Granite. We test input and output lengths from 64 to 4096 tokens and achieve a mean MAPE of 1.79%. Our results show that aligning sequence lengths with these efficiency "sweet spots" reduce energy usage, up to 33.41x, enabling informed truncation, summarization, and adaptive generation strategies in production systems.