Once the properties of secondary structures have been identified, it is only natural to ask how many possible secondary structures can exist for a RNA strand of nucleotides. Note that this question is not asking how many secondary structures are probable for a given set of nucleotides assuming only Watson-Crick pairs. Instead, it asks how many distinct secondary structures could exist over the set of all polynucleotides of length .
Let be the number of secondary structures admissible for a molecule with nucleotides. Clearly, and . Meanwhile , where represents the probability is not paired, while the second term represents all possible pairings given is paired with . This leads us to the recurrence relation
where the first summand represents the cases where is not paired, and the second represents the number of structures when pairs with .
There is no closed form representation for . However it is known that shows asymptotically exponential growth.