Director of Research (if dissertation) or Advisor (if thesis)
Reznick, Bruce A.
Doctoral Committee Chair(s)
Berndt, Bruce C.
Committee Member(s)
Reznick, Bruce A.
Stolarsky, Kenneth B.
Zaharescu, Alexandru
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Stern sequence
recursive sequence
generating function
Fibonacci
Abstract
In this dissertation we define and study a two-parameter family of recursive sequences which we call the bow sequences. The general bow sequence is defined similarly to the Stern sequence, and many of the properties of the bow sequences are related to known properties of the Stern sequence. In particular, we derive the generating function for the general bow sequence, and give interpretations of the generating function for two basic cases. We also determine properties of the bow sequences modulo 2 and 3, and give conjectures for the behavior of the bow sequences modulo d for d
≥4. Finally, we discuss ideas for future research.
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