Some Results Concerning the Padovan Numbers
Abstract
The terms of the relatively recently defined (1994) sequence of the Padovan numbers are generated by a third-order linear recurrence satisfying P0=0, P1=0, P2=1 and Pn+3=Pn+1+Pn. It is known that this sequence is in some ways analogous to the well-known Fibonacci sequence, the terms of which satisfy a second-order linear recurrence. The aim of this paper is to show further the similarities between these two sequences by providing some results known to previous investigators as well as developing new results in the form of identities for the Padovan numbers and their number theoretic properties, while also highlighting their counterparts in the theory of the Fibonacci numbers.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Publication details
- Journal / source
- The Fibonacci Quarterly
- Volume
- 64
- Issue
- 1
- Pages
- 83–107
- Publication date
- 2 January 2026
- Language
- EN