{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16821"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16821","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A sequence related to the Stern sequence","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dennison, Melissa A."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Reznick, Bruce A.","Berndt, Bruce C.","Stolarsky, Kenneth B.","Zaharescu, Alexandru"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T17:58:51Z","date_published":"2010-08-20T17:58:51Z","updated_at":"2026-07-22T22:25:09Z","subjects":["Stern sequence","recursive sequence","generating function","Fibonacci"],"languages":["en"],"rights":["Copyright 2010 Melissa A. Dennison"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16821","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Reznick, Bruce A.","Berndt, Bruce C.","Stolarsky, Kenneth B.","Zaharescu, Alexandru"]},{"key":"dc:creator","label":"Author","values":["Dennison, Melissa A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-08-20T17:58:51Z","2010-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Stern sequence","recursive sequence","generating function","Fibonacci"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Melissa A. Dennison"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16821"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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)"]},{"key":"dc:title","label":"Title","values":["A sequence related to the Stern sequence"]}]}],"canonical_facts":{"dc:contributor":["Reznick, Bruce A.","Berndt, Bruce C.","Stolarsky, Kenneth B.","Zaharescu, Alexandru"],"dc:creator":["Dennison, Melissa A."],"dc:date":["2010-08-20T17:58:51Z","2010-08"],"dc:description":["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)"],"dc:identifier":["http://hdl.handle.net/2142/16821"],"dc:language":["en"],"dc:rights":["Copyright 2010 Melissa A. Dennison"],"dc:subject":["Stern sequence","recursive sequence","generating function","Fibonacci"],"dc:title":["A sequence related to the Stern sequence"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:09Z"}