Calculations for D, the number of ways of dividing a sequence to look for a set of shorter modules. First, partition the number of bases in the sequence n into the number of bases in modules, l, and the number of bases in spacer, s = (n − l). Each possible position of the modules within the longer sequence can be thought of as a particular way of choosing m places to cut the spacer, with the provisions that two cuts cannot occur in the same place and that one cut can occur after the last base of the spacer (i.e., the last module can be at the 3′ end of the sequence). However, the order in which the m cuts are chosen does not matter (even if the cut for the last module was made first, the modules will still be looked for in order). Thus, D is equal to the number of ways of choosing m items from s + 1.
