Succession rules and deco polyominoes

In this paper, we examine the class of "deco" polyominoes and the successio n rule describing their construction. These polyominoes are enumerated acco rding to their directed height by factorial numbers. By changing some aspec ts of the "factorial" rule; we obtain some succession rules that describe v arious "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirl ing numbers of the first and second kind, Narayana and odd index Fibonacci numbers. We wish to point out how the changes made on the original successi on rule yield some new succession rules that produce transcendental, algebr aic and rational generating functions.