Enumerating Binary Strings without r-Runs of Ones
Michael A. Nyblom · RMIT Research Repository (RMIT University Library) · 2012
The number of binary strings of length n containing no substrings consisting of r consecutive ones is examined and shown to be given in terms of a well known integer sequence namely, the r-Fibonacci sequence. In addition, difference equations for the number of zeros and the total number of runs within these binary strings are derived.