Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/16176
Title: Identities relating six members of the Fibonacci family of sequences
Authors: Frontczak, Robert
Гой, Тарас Петрович
Shattuck, Mark
Hoi, Taras
Keywords: Horadam sequence
Fibonacci sequence
Lucas sequence
Pell sequence
Jacobsthal sequence
gibonacci sequence
generating function
Issue Date: 2022
Citation: Frontczak R., Goy T., Shattuck M. Identities relating six members of the Fibonacci family of sequences. Carpathian Mathematical Publications. 2022. Vol. 14(1). P. 6-19.
Abstract: In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences. These identities are obtained as special cases of formulas relating two linear combinations of products of three generalized Fibonacci or Lucas sequences. The latter formulas are in turn obtained from a more general generating function result for the product of three terms coming from second-order linearly recurrent sequences with arbitrary initial values. We employ algebraic arguments to establish our results, making use of the Binet-like formulas of the underlying sequences. Among the sequences for which the aforementioned identities are found include the Fibonacci, Pell, Jacobsthal and Mersenne numbers, along with their associated Lucas companion sequences.
URI: http://hdl.handle.net/123456789/16176
Appears in Collections:Статті та тези (ФМІ)

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