A note on the modified $k$-Fibonacci-like sequence
Commun. Korean Math. Soc. 2016 Vol. 31, No. 1, 1-16
Printed January 31, 2016
Youngwoo Kwon
Korea University
Abstract : 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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