Some Properties of a Third Order Partial Recurrence Relation

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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