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Title:A sequence related to the Stern sequence
Author(s):Dennison, Melissa A.
Director of Research:Reznick, Bruce A.
Doctoral Committee Chair(s):Berndt, Bruce C.
Doctoral Committee Member(s):Reznick, Bruce A.; Stolarsky, Kenneth B.; Zaharescu, Alexandru
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Stern sequence
recursive sequence
generating function
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.
Issue Date:2010-08-20
Rights Information:Copyright 2010 Melissa A. Dennison
Date Available in IDEALS:2010-08-20
Date Deposited:2010-08

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