  The Caporaso-Harris formula gives a recursive algorithm to enumerate delta
nodal degree d curves in P^2. The recursion is obtained in terms of curves of
lower degree that are tangent to a given divisor. This paper presents two
generalizations of this method. The first result is on enumeration of one
cuspidal curves on P^2, and the second result is an extension to the fiber
bundle setting. We solve the question of counting the characteristic number
planar nodal cubics in P^3 by extending the idea of Caporaso-Harris.
