A sequence related to the Stern sequence

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Dennison, Melissa A.

Contributors dc:contributor

• Reznick, Bruce A.
• Berndt, Bruce C.
• Stolarsky, Kenneth B.
• Zaharescu, Alexandru

• Stern sequence
• recursive sequence
• generating function
• Fibonacci

Statement dc:rights

• Copyright 2010 Melissa A. Dennison

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16821

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16821