Enumerating Binary Strings without r-Runs of Ones
نویسنده
چکیده
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. Mathematics Subject Classification: Primary 11B39, Secondary 05A15
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