  We consider a certain abstract of RNA secondary structures, which is closely
related to RNA shapes. The generating function counting the number of the
abstract structures is obtained by means of Narayana numbers and 2-Motzkin
paths, through which we provide an identity related to Narayana numbers and
Motzkin polynomials. Furthermore, we show that a combinatorial interpretation
on 2-Motzkin paths leads to the correspondence between 1-Motkzin paths and RNA
shapes, which facilitates probing further classifications or abstractions of
the shapes. In this paper, we classify the shapes with respect to the number of
components and calculate their asymptotic distributions.
