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 A note on the modified $k$-Fibonacci-like sequence Commun. Korean Math. Soc. 2016 Vol. 31, No. 1, 1-16 https://doi.org/10.4134/CKMS.2016.31.1.1Printed 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 Downloads: Full-text PDF

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