  In this paper we explore enumeration problems related to the number of
reachable configurations in a chip-firing game on a finite connected graph G.
We define an auxiliary notion of debt-reachability and prove that the number of
debt-reachable configurations from an initial configuration with c chips on one
vertex is a quasipolynomial in c. For the cycle graph C_n, we apply these
results to compute a near explicit formula for the number of debt-reachable
configurations. We then derive polynomial asymptotic bounds for the number of
debt-reachable and reachable configurations, and finally provide evidence for a
quasipolynomiality conjecture regarding the number of reachable configurations.
