Generalized Fibonacci Numbers with Indices in Arithmetic Progression and Sum of Their Squares: The Sum Formula ∑nk=0 xkW2mk+j

Soykan, Y¨uksel (2021) Generalized Fibonacci Numbers with Indices in Arithmetic Progression and Sum of Their Squares: The Sum Formula ∑nk=0 xkW2mk+j. Journal of Advances in Mathematics and Computer Science, 36 (6). pp. 30-62. ISSN 2456-9968

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Abstract

In this paper, closed forms of the sum formulas ∑n k=0 xkWmk 2 +j for generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.

Item Type: Article
Subjects: European Repository > Mathematical Science
Depositing User: Managing Editor
Date Deposited: 14 Apr 2023 04:47
Last Modified: 02 Feb 2024 03:50
URI: http://go7publish.com/id/eprint/1784

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