In order to establish natural social synchrony between two humans, two requirements need to be fulfilled. First, the coupling must be bi-directional. The two humans react to each other's actions. Second, natural social bodily synchronization has to be intentional or unintentional. Assuming that these essential aspects of human-human interactions are present, the present paper investigates whether similar bodily synchrony emerges between an interacting human and an artificial agent such as a robot. More precisely, we investigate whether the same human unintentional rhythmic entrainment and synchronization is present in Human Robot Interaction (HRI). We also evaluate which model (e.g., an adaptive vs non adaptive robot) better reproduces such unintentional entrainment. And finally, we compare interagent coordination stability of the HRI under 1) unidirectional (robot with fixed frequency) versus bidirectional (robot with adaptive frequency) rhythmic entrainment and 2) human intentional versus unintentional coupling. Fifteen young adults made vertical arm movements in front of the NAO robot under five different conditions of intentional/unintentional and unidirectional/bidirectional interactions. Consistent with prior research investigating human-human interpersonal coordination, when humans interact with our robot, (i) unintentional entrainment was present, (ii) bi-directional coupling produced more stable inphase unintentional and intentional coordination, (iii) and intentional coordination was more stable than unintentional coordination. To conclude, this study provides a foundation for modeling future social robots involving unintentional and bidirectional synchronizationaspects which seem to enhance humans' willingness to interact with robots.