  We report a numerical calculation of the total number of disordered jammed
configurations $\Omega$ of $N$ repulsive, three-dimensional spheres in a fixed
volume $V$. To make these calculations tractable, we increase the computational
efficiency of the approach of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011))
and Asenjo et al. (Phys. Rev. Lett. 112, 098002 (2014)) and we extend the
method to allow computation of the configurational entropy as a function of
pressure. The approach that we use computes the configurational entropy by
sampling the absolute volume of basins of attraction of the stable packings in
the potential energy landscape. We find a surprisingly strong correlation
between the pressure of a configuration and the volume of its basin of
attraction in the potential energy landscape. This relation is well described
by a power law. Our methodology to compute the number of minima in the
potential energy landscape should be applicable to a wide range of other
enumeration problems in statistical physics, string theory, cosmology and
machine learning, that aim to find the distribution of the extrema of a scalar
cost function that depends on many degrees of freedom.
