An unusual conductance sequenceEffects of correlations between electrons are enhanced in systems of reduced dimensions. The two-dimensional interface between two oxide materials, lanthanum aluminate (LaAlO3) and strontium titanate (SrTiO3), exhibits magnetism and superconductivity. In even lower-dimensional systems fabricated in similar heterostructures, electrons can pair without going superconducting. Briggeman et al. have now observed another exotic effect in LaAlO3/SrTiO3 waveguides: At certain magnetic fields, the conductance in these one-dimensional systems exhibits steps of an unconventional sequence. To understand the experimental data, the researchers used a model that accounted for interactions between electrons and found that the phenomenology was consistent with the formation of a series of correlated phases characterized by bound states of three or more electrons.Science, this issue p. 769One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO3/SrTiO3) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e2/h, where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.