A note on sum of k-th power of Horadam's sequence

2003/02/02 by Toufik Mansour, Mansour, Toufik
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO

paper · pdf · doi:10.48550/arxiv.math/0302015

5 pages

arxiv created 2003/02/02 · openalex publication_date 2003/02/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w_n+2=pw_n+1+qw_n for n≥0 with w₀=a and w₁=b. In this paper we find an explicit expression, in terms of determinants, for ∑_n≥0 w_n^kxⁿ for any k≥1. As a consequence, we derive all the previously known results for this kind of problems, as well as many new results.

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