Nucleic acid secondary structure models usually exclude pseudoknots due to the difficulty of treating these non-nested structures efficiently in structure prediction and partition function algorithms. Here, the standard secondary structure energy model in extended to include the most physically relevant pseudoknots. We describe an O(N^5) dynamic programming algorithm, where N is the length of the strand, for computing the partition function and minimum energy structure over this class of secondary structures. Hence, it is possible to determine the probability of sampling the lowest energy structure, or any other structure of particular interest. This capability motivates the user of the partition function for the design of DNA or RNA molecules for bioengineering applications