Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2016; 31(1): 1-16

Printed January 31, 2016

https://doi.org/10.4134/CKMS.2016.31.1.1

Copyright © The Korean Mathematical Society.

A note on the modified $k$-Fibonacci-like sequence

Youngwoo Kwon

Korea University

Abstract

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The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the modified $k$-Fibonacci-like sequence and prove Binet's formula for this sequence and then use it to introduce and prove the Catalan, Cassini, and d'Ocagne identities for the modified $k$-Fibonacci-like sequence. Also, the ordinary generating function of this sequence is stated.

Keywords: $k$-Fibonacci sequence, $k$-Fibonacci-like sequence, Binet's formula

MSC numbers: Primary 11B39, 11B75

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