The introduction of artificial intelligence (AI) agents into human group settings raises essential questions about how these novel participants influence cooperative social norms. While previous studies on human-AI cooperation have primarily focused on dyadic interactions, little is known about how integrating AI agents affects the emergence and maintenance of cooperative norms in small groups. This study addresses this gap through an online experiment using a repeated four-player Public Goods Game (PGG). Each group consisted of three human participants and one bot, which was framed either as human or AI and followed one of three predefined decision strategies: unconditional cooperation, conditional cooperation, or free-riding. In our sample of 236 participants, we found that reciprocal group dynamics and behavioural inertia primarily drove cooperation. These normative mechanisms operated identically across conditions, resulting in cooperation levels that did not differ significantly between human and AI labels. Furthermore, we found no evidence of differences in norm persistence in a follow-up Prisoner's Dilemma, or in participants' normative perceptions. Participants' behaviour followed the same normative logic across human and AI conditions, indicating that cooperation depended on group behaviour rather than partner identity. This supports a pattern of normative equivalence, in which the mechanisms that sustain cooperation function similarly in mixed human-AI and all human groups. These findings suggest that cooperative norms are flexible enough to extend to artificial agents, blurring the boundary between humans and AI in collective decision-making.