Sum of the Squares of the Extended (k, t)–Fibonacci Numbers

Sergio Falcon

doi:10.20944/preprints202408.1150.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 14 August 2024 / Approved: 15 August 2024 / Online: 15 August 2024 (12:21:32 CEST)

{In two previous articles, the extended $(k, t)$--Fibonacci numbers were presented and some of their properties were studied, both in general and particularizing them for the Leonardo numbers. In a second article we study the sum of the extended $(k, t)$--Fibonacci numbers as well as the sums of these odd and even numbers.\\ In this article we study the sum of the squares of these numbers with their properties as well as the generating function, the recurrence relation and the Binet formula.\\ Finally we particularize these results for the generalized $t$--Leonardo numbers

k–Fibonacci numbers; binet identity; recurrence relation; generating function; Leonardo numbers

Computer Science and Mathematics, Applied Mathematics

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Sum of the Squares of the Extended (k, t)–Fibonacci Numbers

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