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Reznick, Bruce A. Berndt, Bruce C. Reznick, Bruce A. Stolarsky, Kenneth B. Zaharescu, Alexandru Dennison, Melissa A. 2010-08-20T17:58:51Z 2010-08-20T17:58:51Z 2010-08-20T17:58:51Z 2010-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-23T23:00:52Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Dennison_Melissa.pdf: 712973 bytes, checksum: f0628dd5bf77ab484057db9373723aad (MD5) Made available in DSpace on 2010-08-20T17:58:51Z (GMT). No. of bitstreams: 2 Dennison_Melissa.pdf: 712973 bytes, checksum: f0628dd5bf77ab484057db9373723aad (MD5) license.txt: 4066 bytes, checksum: f77c6e74f3f8e155cc011b80c9392cc1 (MD5) http://hdl.handle.net/2142/16821 en Copyright 2010 Melissa A. Dennison Stern sequence recursive sequence generating function Fibonacci A sequence related to the Stern sequence Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD