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Combining strong coupling and hopping expansion one can derive adimensionally reduced effective theory of lattice QCD. This theory has areduced sign problem, is amenable to analytic evaluation and was successfullyused 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 $N_c$up to $\kappa^4$. The inclusion of gauge corrections is also investigated. Wefind that the onset transition to finite baryon number density steepens withgrowing $N_c$ even for $T \neq 0$. This suggests that in the large $N_c$ limitthe onset transition is first order up to the deconfinement transition. Beyondthe onset, the pressure is shown to scale as $p \sim N_c$ through three ordersin the hopping expansion, which is characteristic for a phase termed quarkyonicmatter in the literature.

Large $N_c$ behaviour of lattice QCD in the heavy dense regime