Journal of Integer Sequences, Vol. 28 (2025), Article 25.8.8

Identities and Hadamard Product of the Generalized Fibonacci, Lucas, Catalan, and Harmonic Numbers


Vladimir V. Kruchinin and Maria Y. Perminova
Tomsk State University of Control Systems and Radioelectronics
Tomsk
Russian Federation

Abstract:

We consider properties of the generalized Fibonacci and Lucas numbers. We obtain identities related to the generalized Fibonacci, Lucas, Catalan, and harmonic numbers. We also derive explicit expressions for the generating functions of the Hadamard products of the generalized Fibonacci, Lucas, Catalan, and harmonic numbers.

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(Concerned with sequences A000032 A000045 A000129 A001045 A001076 A002203 A002605 A005668 A006130 A006190 A006497 A007482 A008459 A014448 A014551 A015518 A030195 A041025 A052918 A054413 A075118 A080040 A085447 A086594 A086902 A087130 A087798 A099371 A102345 A119694 A172012 A206776 A372216.)

Received June 5 2024; revised versions received June 10 2024; April 30 2025. Published in Journal of Integer Sequences, December 15 2025.

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