Binary words avoiding a pattern and marked succession rule

Enumeration and construction of particular binary words avoiding the pattern $1^{j+1}0^j$. By means of the theory of Riordan arrays, the enumeration problem is solved and a particular succession rule, called jumping and marked succession rule, is used to 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.