We characterize the sequence of bifurcations generated by ac fields in a nematic layer held between unidirectionally rubbed ITO electrodes. The material, which possesses a negative dielectric anisotropy epsilon(a) and an inversion temperature for electrical conductivity anisotropy sigma(a), exhibits a monostable tilted alignment near T-IN, the isotropic-nematic point. On cooling, an anchoring transition to the homeotropic configuration occurs close to the underlying smectic phase. The field experiments are performed for (i) negative sigma(a) and homeotropic alignment, and (ii) weakly positive sigma(a) and nearly homeotropic alignment. Under ac driving, the Freedericksz transition is followed by bifurcation into various patterned states. Among them are the striped states that seem to belong to the dielectric regime and localized hybrid instabilities. Very significantly, the patterned instabilities are not excited by dc fields, indicating their possible gradient flexoelectric origin. The Carr-Helfrich mechanism-based theories that take account of flexoelectric terms can explain the observed electroconvective effects only in part.