A sequence related to the Stern sequence

Stern sequence;recursive sequence;generating function;Fibonacci

Dennison, Melissa A.

关键词: Stern sequence;    recursive sequence;    generating function;    Fibonacci;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16821/Dennison_Melissa.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.