Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences

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dc.creatorStanica, Pantelimon
dc.date2000-10-15
dc.date.accessioned2026-07-07T04:38:02Z
dc.date.available2026-07-07T04:38:02Z
dc.descriptionIn 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.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0010149
dc.identifierhttp://arxiv.org/abs/math/0010149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60131
dc.subjectCombinatorics
dc.subject05A10; 05A19; 11B37; 11B39; 11B65
dc.titleGenerating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences
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