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.
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 6) |
| DOI | 10.11648/j.pamj.20130206.11 |
| Page(s) | 174-178 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2013. Published by Science Publishing Group |
Fibonacci Sequence, Pell – Padovan’s Sequence, Generating Function, Binet Formula, Matrix Methods
| [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. |
APA Style
Goksal Bilgici. (2013). Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods. Pure and Applied Mathematics Journal, 2(6), 174-178. https://doi.org/10.11648/j.pamj.20130206.11
ACS Style
Goksal Bilgici. Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods. Pure Appl. Math. J. 2013, 2(6), 174-178. doi: 10.11648/j.pamj.20130206.11
AMA Style
Goksal Bilgici. Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods. Pure Appl Math J. 2013;2(6):174-178. doi: 10.11648/j.pamj.20130206.11
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Download@article{10.11648/j.pamj.20130206.11,
author = {Goksal Bilgici},
title = {Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {6},
pages = {174-178},
doi = {10.11648/j.pamj.20130206.11},
url = {https://doi.org/10.11648/j.pamj.20130206.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.11},
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.},
year = {2013}
}
TY - JOUR T1 - Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods AU - Goksal Bilgici Y1 - 2013/11/30 PY - 2013 N1 - https://doi.org/10.11648/j.pamj.20130206.11 DO - 10.11648/j.pamj.20130206.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 174 EP - 178 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20130206.11 AB - 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. VL - 2 IS - 6 ER -
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