2000/10/15 by Pantelimon Stănică, Pantelimon Stanica, Stanica, Pantelimon
Mathematics · #05A10 #05A19 #11B37 #11B39 #11B65 #Algebraic and Geometric Analysis #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.CO #msc:05A10 #msc:05A19 #msc:11B37 #msc:11B39 #msc:11B65
paper · pdf · doi:10.48550/arxiv.math/0010149
15 pages
arxiv created 2000/10/15 · openalex publication_date 2000/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find closed form for the generating function of powers of any non-degenerate second-order recurrence sequence, completing a study begun by Carlitz and Riordan in 1962. Moreover, we generalize a theorem of Horadam on partial sums involving such sequences. Also, we find closed forms for weighted (by binomial coefficients) partial sums of powers of any non-degenerate second-order recurrence sequences. As corollaries we give some known and seemingly unknown identities and derive some very interesting congruence relations involving Fibonacci and Lucas sequences.