As part of Dr. Nathan Kahl’s Junior Seminar class for mathematics majors, the students worked on teams to solve published open mathematics problems. Senior Mathematics majors Dominic Kozlowski and Anayelli Vigo have had their solution to “Ordered Partitions with All Parts Odd” published as the featured solution in Mathematics Magazine, Volume 96, issue 4.
The problem statement is: Let f (n) denote the number of ordered partitions of a positive integer n such that all of the parts are odd. For example, f (5) = 5, since 5 can be written as 5, 3 + 1 + 1, 1 +3 + 1, 3 + 1 + 1, and 1 + 1 + 1 + 1 + 1. Determine f (n).
