Journal of Integer Sequences, Vol. 27 (2024), Article 24.7.2

Finite Sums Involving Fibonacci and Lucas Numbers


Fatima Zohra Bensaci
LA3C, Faculty of Mathematics
USTHB, Algiers
Algeria

Rachid Boumahdi
National Higher School of Mathematics
Sidi Abdallah, Algiers
Algeria

Laala Khaldi
LIM Laboratory
Department of Mathematics
University of Bouira
10000 Bouira
Algeria

Abstract:

In this paper, we introduce several identities related to Fibonacci and Lucas numbers, extending the results established by Byrd in 1975. Moreover, we derive some identities involving Fibonacci, Lucas, Bernoulli, Euler, Genocchi, and Stirling numbers. Our main tools are linear operators and their properties.

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(Concerned with sequences A000032 A000045 A008275 A008277 A036968 A048994 A122045.)

Received July 23 2024; revised version received August 19 2024. Published in Journal of Integer Sequences, August 19 2024.

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