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

#### Abstract

**In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is known as 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.**

#### Full Text:

PDF#### References

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

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

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

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

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

. 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.

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

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

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

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

. 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.

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

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

### Refbacks

- There are currently no refbacks.

**MAYFEB Journal of Electrical and Computer Engineering****MAYFEB TECHNOLOGY DEVELOPMENT****Toronto, Ontario, Canada**