  In this paper we study the enumeration and the construction of particular
binary words avoiding the pattern $1^{j+1}0^j$. By means of the theory of
Riordan arrays, we solve the enumeration problem and we give a particular
succession rule, called jumping and marked succession rule, which describes the
growth of such words according to their number of ones. Moreover, the problem
of associating a word to a path in the generating tree obtained by the
succession rule is solved by introducing an algorithm which constructs all
binary words and then kills those containing the forbidden pattern.
