  This article computes the generating functions of the Betti numbers of the
moduli space of stable sheaves of rank 3 on the projective plane P2 and its
blow-up. Wall-crossing is used to obtain the Betti numbers on the blow-up.
These can be derived equivalently using flow trees, which appear in the physics
of BPS-states. The Betti numbers for P2 follow from those for the blow-up by
the blow-up formula. The generating functions are expressed in terms of modular
functions and indefinite theta functions.
