#### Award Date

May 2018

#### Degree Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mathematical Sciences

#### First Committee Member

Peter Shiue

#### Second Committee Member

Derrick DuBose

#### Third Committee Member

Arthur Baragar

#### Fourth Committee Member

Yi-Tung Chen

#### Number of Pages

112

#### Abstract

In this Masters thesis, we examine linear divisible sequences. A linear divisible sequence is any sequence {an}n≥0 that can be expressed by a linear homogeneous recursion relation that is also a divisible sequence. A sequence {an}n≥0 is called a divisible sequence if it has the property that if n|m, then an|am. A sequence of numbers {an}n≥0 is called a linear homogeneous recurrence sequence of order m if it can be written in the form

an+m = p1an+m−1 + p2an+m−2 + · · · + pm−1an+1 + pman, n ≥ 0,

for some constants p1, p2, ..., pm with pm = 0 and initial conditions a0, a1, ..., am−1. We focus on taking products, powers, and products of powers of second order linear divisible sequences in order to construct higher order linear divisible sequences. We hope to find a pattern in these constructions so that we can easily form higher order linear divisible sequence.

#### Disciplines

Mathematics

#### Language

English

#### Repository Citation

Trendell, Sean, "Notes on Linear Divisible Sequences and Their Construction: A Computational Approach" (2018). *UNLV Theses, Dissertations, Professional Papers, and Capstones*. 3336.

https://digitalscholarship.unlv.edu/thesesdissertations/3336