Combining strong coupling and hopping expansion one can derive a dimensionally reduced effective theory of lattice QCD. This theory has a reduced sign problem, is amenable to analytic evaluation and was successfully used to study the cold and dense regime of QCD for sufficiently heavy quarks. We show results from the evaluation of the effective theory for arbitrary Nc up to κ4. The inclusion of gauge corrections is also investigated. We find that the onset transition to finite baryon number density steepens with growing Nc even for T≠0. This suggests that in the large Nc limit the onset transition is first order up to the deconfinement transition. Beyond the onset, the pressure is shown to scale as p∼Nc through three orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature.