The 2λ−O oscillatory mode of cellular solidification patterns is studied in thin samples of a succinonitrile-acrylonitrile transparent alloy. The origin and the nature of oscillations are revisited and discussed by combining experiment with 3D phase-field numerical simulations. The existence domain of 2λ−O oscillations and the evolution of their period with growth velocity are determined and compared. Simulations evidence transversal solute fluxes between neighbor cells as an essential feature of cell dynamics. A solute balance model in which transversal fluxes are crucial for oscillations recovers the emergence of a 2λ−O mode and its period-velocity relationship. It thus confirms the fundamental role of transversal fluxes and provides a complete coherent description of the physical mechanisms of 2λ−O oscillations. Parametric excitations are finally used to force 2λ−O oscillations beyond their stability domain and highlight the nature of the underlying oscillator, especially its non-linearity responsible for intermittent oscillations and complex behavior in the resonance band.