Some Properties of a Third Order Partial Recurrence Relation

Year 2021, Volume: 34 Issue: 4, 1089 - 1094, 01.12.2021

Anthony G. Shannon , Ömür Deveci

https://doi.org/10.35378/gujs.770440

Abstract

This paper explores a connection between third order recursive sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions. It does this with a partial recurrence relation which is related to the original third order recurrence relation, and raises a related conjecture.

Keywords

Fibonacci numbers, Tribonacci numbers, Partial quotients, Euclidean algorithm

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