With the explosive growth of video data, video summarization which converts long-time videos to key frame sequences has become an important task in information retrieval and machine learning. Determinantal point processes (DPPs) which are elegant probabilistic models have been successfully applied to video summarization. However, existing DPP-based video summarization methods suffer from poor efficiency of outputting a specified size summary or neglecting inherent sequential nature of videos. In this paper, we propose a new model in the DPP lineage named k-SDPP in vein of sequential determinantal point processes but with fixed user specified size k. Our k-SDPP partitions sampled frames of a video into segments where each segment is with constant number of video frames. Moreover, an efficient branch and bound method (BB) considering sequential nature of the frames is provided to optimally select k frames delegating the summary from the divided segments. Experimental results show that our proposed BB method outperforms not only k-DPP and sequential DPP (seqDPP) but also the partition and Markovian assumption based methods.