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Generalized Order–k Pell–Padovan–Like Numbers by Matrix Methods
Pure and Applied Mathematics Journal
Volume 2, Issue 6, December 2013, Pages: 174-178
Received: Sep. 25, 2013; Published: Nov. 30, 2013
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Goksal Bilgici, Department of Computer Education and Instructional Technology, Kastamonu University, Kastamonu, Turkey
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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.
Fibonacci Sequence, Pell – Padovan’s Sequence, Generating Function, Binet Formula, Matrix Methods
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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
B.A. Brousseau, "Fibonacci Numbers and Geometry", Fibonacci Quart., vol. 10, no.3, pp. 303-318, 1972.
M.C. Er, "Sums of Fibonacci Numbers by Matrix Method", Fibonacci Quart., vol.22, no.3, pp. 204-207 1984.
D. Kalman, "Generalized Fibonacci Numbers by Matrix Method", Fibonacci Quart., vol. 20, no.1,pp. 73-76, 1982.
K. Kaygisiz and D. Bozkurt, "k-Generalized Order-k Perrin Number Presentation by Matrix Method", ArsCombinatoria, vol.105, pp. 95-101, 2012.
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.
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.
F. Yilmaz, D. Bozkurt, "Some Properties of Padovan Sequence by Matrix Method", ArsCombinatoria, vol. 104, pp. 149-160, 2012.
[8], The Online Encyclopedia of Integer Sequences, Series: A008346.
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