Home > RHUMJ > Vol. 5 (2004) > Iss. 2

#### Article Title

A Search for Patterns in a Sequence of Integers: Proving Trends in a Recurrence Relation

#### Abstract

Let {f(n} be the sequence of integers determined by the recurrence relation f(n+2) equivalent to 2f(n+1) - f(n) (mod(n+2)) with f(n) greater than or equal to 0 and less than n for every integer n greater than or equal to m, where m is a certain positive integer with initially assigned arbitrary integers f(m) and f(m+1). We investigate how the sequence {f(n} increases or decreases. We call a maximal increasing or decreasing subsequence of consecutive elements of the sequence a run. We show that each run is an arithmetic progression and that the common difference in an increasing run is one more than the common difference in the previous increasing run, and similary for decreasing runs.

#### Recommended Citation

Saify, Qaiser
(2004)
"A Search for Patterns in a Sequence of Integers: Proving Trends in a Recurrence Relation,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 5
:
Iss.
2
, Article 10.

Available at:
http://scholar.rose-hulman.edu/rhumj/vol5/iss2/10