Eliel Sosis
Pronouns: he/him/his
Research Mentor(s):
Co-Presenter: Davis, Sophia
Research Mentor School/College/Department: Mathematics / NonUM
Presentation Date: April 20
Presentation Type: Poster
Session: Session 2 – 11am – 11:50am
Room: League Ballroom
Authors: Steven Miller, Eliel Sosis, Sophia Davis Davis
Presenter: 120
Abstract
There is a growing literature on reciprocal sums of recurrence relations with constant coefficients and fixed depth, such as Fibonacci numbers, products of such numbers, and balancing numbers. Balancing numbers are numbers n such that the sum of the integers less than n equal the sum of the r integers immediately after, for some r which is called the balancer of n. If n is included in the summation, we have the cobalancing numbers, and r is called the cobalancer of n. We generalize to reciprocal sums of depth two recurrence sequences with arbitrary coefficients, and show our method provides an alternative proof of some existing results. We define (a, b) balancing and cobalancing numbers, where a and b are constants that multiply the left-hand side and right-hand side respectively. We then found recurrence relations describing sequences of (a, b) balancing and cobalancing numbers and their respective balancers and cobalancers for given coefficients a and b. We show that for balancing numbers, coefficients (3, 1) are unique such that every integer is a balancing number, and proved there does not exist an analogous set of coefficients for cobalancing numbers. We also found patterns for certain coefficients that have no balancing or cobalancing numbers.
Interdisciplinary, Physical Sciences
