#### On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

Full Text (PDF, 376KB), PP.20-36

##### Author(s)

1. School of Studies in Mathematics, Vikram University Ujjain, India.

* Corresponding author.

Received: 21 Feb. 2017 / Revised: 28 Apr. 2017 / Accepted: 8 Jun. 2017 / Published: 8 Nov. 2017

##### Index Terms

Fibonacci Sequence, Lucas Sequence, Generalization of Fibonacci Sequence, Matrix Method

##### Abstract

In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.

##### Cite This Paper

Arfat Ahmad Wani, V. H. Badshah,"On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.3, No.4, pp.20-36, 2017.DOI: 10.5815/ijmsc.2017.04.03

##### Reference

[1]Cerda, G., “Matrix Methods in Horadam Sequences”, Boletín de Matemáticas, 19(2), 2012, pp.97-106.

[2]Čerin, Z., “On Factors of Sums of Consecutive Fibonacci and Lucas Numbers”, Annales Mathematicae et Informaticae, 41, 2013, pp. 19-25.

[3]Dasdemir, A., “On the Pell, Pell-Lucas and Modified Pell Numbers by Matrix Method”, Applied Mathematical Sciences, 5(64), 2011, pp.3173-3181.

[4]Horadam, A. F., “Basic Properties of a Certain Generalized Sequence of Numbers”, The Fibonacci Quarterly, 3(3), 1965, pp.161-176.

[5]Jun, S. P. and Choi, K. H., “Some Properties of the Generalized Fibonacci Sequence by Matrix Methods Methods”, The Korean Journal of Mathematics, 24(4), 2016, pp.681-691.

[6]Keskin, R. and Demirtürk, B., “Some New Fibonacci and Lucas Identities by Matrix Methods”, International Journal of Mathematical Education in Science and Technology, 41(3), 2010, pp.379-387.

[7]Kilic, E., “Sums of Generalized Fibonacci Numbers by Matrix Methods”, Ars Combinatoria, 84, 2007, pp.23-32.

[8]Koken, F. and Bozkurt, D., “On Lucas Numbers by the Matrix Method”, Hacettepe Journal of Mathematics and Statistics, 39(4), 2010, pp.471-475.

[9]Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2011.

[10]Posamentier, A. S., The Fabulous Fibonacci Numbers, Prometheus Books, 2007.

[11]Singh, B., Bhadouria, P. and Sikhwal, O., “Generalized Identities Involving Common Factors of Fibonacci and Lucas Numbers”, International Journal of Algebra, 5(13), 2011, pp.637-645.

[12]Thongmoon, M., 2009, “Identities for the Common Factors of Fibonacci and Lucas Numbers”, International Mathematical Forum, 4(7), 2009, pp. 303-308.

[13]Vajda, S., Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Courier Corporation, 1989.