Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods

Goksal Bilgici

doi:10.11648/j.pamj.20130206.11

Home

Journals

Special Issues

Books

Submission

Services

Pure and Applied Mathematics Journal

Home

Archive

2020, Volume 9

Vol. 9, Issue 6, Dec.

Vol. 9, Issue 5, Oct.

Vol. 9, Issue 4, Aug.

Vol. 9, Issue 3, Jun.

Vol. 9, Issue 2, Apr.

Vol. 9, Issue 1, Feb.

2019, Volume 8

2018, Volume 7

2017, Volume 6

2016, Volume 5

2015, Volume 4

2014, Volume 3

2013, Volume 2

2012, Volume 1

Special Issues

Propose a Special Issue Special Issue Guidelines

Home / Journals / Mathematics & Statistics / Pure and Applied Mathematics Journal / Article

Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods

< Previous Article

Pure and Applied Mathematics Journal
Volume 2, Issue 6, December 2013, Pages: 174-178
Received: Sep. 25, 2013; Published: Nov. 30, 2013

Views 3782 Downloads 226

Author

Goksal Bilgici, Department of Computer Education and Instructional Technology, Kastamonu University, Kastamonu, Turkey

Article Tools

Abstract

PDF

Follow on us

Abstract

Weconsider the third – order recurrence relation Q_n=2Q_(n-2)+Q_(n-3) with initial conditionsQ_0=1,Q_1=0 "and" Q_2=2 and define these numbers as Pell – Padovan – like numbers.We extend this definition generalized order – k Pell – Padovan – like numbers and give some relations between thesenumbers and the Fibonacci numbers. Wealso obtain some relations of thesenumbers and matrices by using matrix methods.

Keywords

Fibonacci Sequence, Pell – Padovan’s Sequence, Generating Function, Binet Formula, Matrix Methods

To cite this article

Goksal Bilgici, Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods, Pure and Applied Mathematics Journal. Vol. 2, No. 6, 2013, pp. 174-178. doi: 10.11648/j.pamj.20130206.11

References

[1]

B.A. Brousseau, "Fibonacci Numbers and Geometry", Fibonacci Quart., vol. 10, no.3, pp. 303-318, 1972.

[2]

M.C. Er, "Sums of Fibonacci Numbers by Matrix Method", Fibonacci Quart., vol.22, no.3, pp. 204-207 1984.

[3]

D. Kalman, "Generalized Fibonacci Numbers by Matrix Method", Fibonacci Quart., vol. 20, no.1,pp. 73-76, 1982.

[4]

K. Kaygisiz and D. Bozkurt, "k-Generalized Order-k Perrin Number Presentation by Matrix Method", ArsCombinatoria, vol.105, pp. 95-101, 2012.

[5]

A.G. Shannon, A.F. Horadam and P. G. Anderson, "The Auxiliary Equation Associated with the Plastic Number", Notes on Number Theory and Discrete Mathematics, vol.12, no.1, pp. 1-12, 2006.

[6]

A.G. Shannon, P G. Anderson and A.F. Horadam, "Properties of Cordonnier, Perrin and Van der Laan Numbers", International Journal of Mathematical Education in Science & Technology, vol. 37, no.7, pp. 825-831, 2006.

[7]

F. Yilmaz, D. Bozkurt, "Some Properties of Padovan Sequence by Matrix Method", ArsCombinatoria, vol. 104, pp. 149-160, 2012.

[8]

http://oeis.org, The Online Encyclopedia of Integer Sequences, Series: A008346.

PUBLICATION SERVICES

JOIN US

Join as an Editor-in-Chief

Join as an Editorial Member