# Number Theory Seminar

**Presented by: Larry Ericksen**

**Title: “Generalized Stern Polynomials: Their Recursions and Continued Fractions”**

**Abstract: **

This talk describes the polynomial analogue in b variables related to the Stern number sequences which interpret the number of ways to write a positive integer as the restricted sum of powers of integer base b. Wepresent recursions and generating functions for these polynomials which

explicitly specify those hyper b-ary representations.

Lucas sequences, like those of Fibonacci and Pell, are identified within the generalized Stern number sequences. Then as polynomial analogues, the continued fractions associated with the Lucas sequences are expressed as ratios of their corresponding polynomials.

#### Category

All Events

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#### Location

Seminar Room #227, Chase Building