Korean J. Math. Vol. 22 No. 3 (2014) pp.443-454
DOI: https://doi.org/10.11568/kjm.2014.22.3.443

Linearlization of generalized Fibonacci sequences

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Published: Sep 25, 2014
Keywords:
generalized Fibonacci sequences, Binet's formula, companion matrix, Cassini's identity.
Mathematics Subject Classification:
11B39.

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Young Ho Jang
Inha University
Sang Pyo Jun

Abstract

In this paper, we give linearization of generalized Fibonacci sequences $\{g_n\}$ and $\{q_n\}$, repectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the $n$th power of a companion matrix of $\{g_n\}$ and $\{q_n\}$, repectively. Then we re-prove the Cassini's identity for $\{g_n\}$ and $\{q_n\}$, respectively.


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Supporting Agencies

Funding for this paper was provided by Namseoul University.

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