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This article computes the generating functions of the Betti numbers of themoduli space of stable sheaves of rank 3 on the projective plane P2 and itsblow-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 physicsof BPS-states. The Betti numbers for P2 follow from those for the blow-up bythe blow-up formula. The generating functions are expressed in terms of modularfunctions and indefinite theta functions.

The Betti numbers of the moduli space of stable sheaves of rank 3 on P2