Determinantal Identities of Fibonacci, Fibonacci Like and Lucas Numbers

Sanjay Harne¹, V.H. Badshah² and Sapna Sethiya^3,

¹Government College, Kannod(M.P.), India

²School of studies in Mathematics

³Vikram University Ujjain, India

Cite this paper:
Sanjay Harne, V.H. Badshah and Sapna Sethiya. Determinantal Identities of Fibonacci, Fibonacci Like and Lucas Numbers. Turkish Journal of Analysis and Number Theory. 2014; 2(4):110-112. doi: 10.12691/tjant-2-4-1

Abstract

Determinants have played a significant part in various areas in mathematics. For instance, they are quite useful in the analysis and solution of system of linear equations. There are different perspectives on the study of determinant. In this paper we present some determinant identities of Fibonacci and Lucas numbers.

Keywords:
fibonacci number lucas number fibonacci like sequence

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References:

[1]	Benjamin A., Cameron N. and Quinn J.: Fibonacci Determinants- A Combinatorial Approach, Fibonacci Quarterly, 39-55 (1), 2007, Vol 45.
[2]	Bicknell-Johnson M. and Spears C. P.:Classes Of Identities For the Generalized Fibonacci number Gn= Gn-1 + Gn-2, n ≥ 2. from Matrices with Constantvalued Determinants, Fibonacci Quarterly, 121-128 (2), 1996, Vol. 34.
[3]	B. Singh, O. Sikhwal, and S. Bhatnagar, Fibonacci-Like Sequence and its properties, Int.J. Contemp Math.Sciences, Vol.5, 2010, No.18, 857-868.
[4]	Cahill N. and Narayan D.:Fibonacci and Lucas numbers s Tridigonal Matrix Determinants, Fibonacci Quarterly, 216-221 (3), 2004, Vol. 42.
[5]	Koshy T.:Fibonacci and Lucas Numbers with Applications, Wiley, 2001.
[6]	Krattenthaler C.: Advanced determinant calculus, Seminaire Lotharingien Combin, Article, b42q, 67, 1999.
[7]	Krattenthaler C.: Advanced determinant calculus: A Complement, Liner Algebra Appl., 68-166.
[8]	Macfarlane A. J.: Use of Determinants to Present Identities Involving Fiboncci and Related Numbers, Fibonacci Quarterly, 68-7648(1), 2010, Vol. 48.
[9]	Spivey M. Z.: Fibonacci Identities via the Determinant sum property, College Mathematics Journal, 286-289 (4), 2006, Vol. 37.