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https://hdl.handle.net/20.500.11851/11534
Title: | BINOMIAL SUMS INVOLVING SECOND-ORDER LINEARLY RECURRENT SEQUENCES | Authors: | Campbell, J.M. Kiliç, E. |
Publisher: | Fibonacci Association | Abstract: | Consider the sequences (Un : n ∈ N0) and (Vn : n ∈ N) satisfying the secondorder linear recurrences Un = pUn-1+Un-2 and Vn = pVn-1+Vn-2 with the initial conditions U0 = 0, U1 = 1, V0 = 2, and V1 = p. We explore the problem of evaluating binomial sums involving products consisting of entries in the U- and V -sequences. We apply a hypergeometric approach, inspired by Dilcher's work on hypergeometric identities for Fibonacci numbers, to obtain many new identities for sums involving U and V and products of binomial coefficients, including a non-hypergeometric analogue of Dixon's binomial identity. © 2024 Fibonacci Association. All rights reserved. | URI: | https://hdl.handle.net/20.500.11851/11534 | ISSN: | 0015-0517 |
Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection |
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