Sequences related to the Pell generalized equation

2003/04/04 by Mario Catalani, Catalani, Mario
Mathematics · Physics and Astronomy · #11B39 #11D09 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.CO #math.NT #msc:11B39 #msc:11D09

paper · pdf · doi:10.48550/arxiv.math/0304062

Fixed some minor typos

openalex publication_date 2003/04/04 · arxiv created 2003/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider sequences of the type A_n=6A_n-1-A_n-2, A₀=r, A₁=s (r and s integers) and show that all sequences that solve particular cases of the Pell generalized equation are expressible as a constant times one of four particular sequences of the same type.

Related

• On Generalizations of the Pell Sequence
• Common terms of generalized Pell and Narayana's cows sequences
• Sum of terms of recurrence sequences in the solution sets of generalized Pell equations
• Some properties of generalized k-Pell sequences
• Sum of Consecutive Terms of Pell and Related Sequences