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Year 2016 ,
Volume: 3 Issue: 2, 99 - 104, 31.12.2016
Ahmet Daşdemir
References
1. Stakhov AP. A generalization of the Fibonacci Q-matrix. National Academy of Sciences of Ukraine 9 (1999) 46-49.
2. Stakhov AP, Rozin B. Theory of Binet formulas for Fibonacci and Lucas p-numbers. Chaos Solitions and Fractals 27 (2006) 1162-1177.
3. Kilic E. The Binet formula, sum and representations of generalized Fibonacci p-numbers. European Journal of Combinatorics 29 (2008) 701-711.
4. Horadam AF. Jacobsthal Representation Numbers. Fibonacci Quarterly 34 (1996) 40-54.
5. Cerin Z. Sums of Squares and Products of Jacobsthal Numbers. Journal of Integer Sequences 10 (2007) Article 07.2.5.
6. Chen WYC, Louck JD. The combinatorial power of the companion matrix. Linear Algebra and its Applications 232 (1996) 261-78.
7. Koken F, Dozkurt D. On the Jacobsthal Numbers by Matrix Methods. International Journal of Contemporary Mathematical Sciences 3(13) (2008) 605-614.
The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence
Year 2016 ,
Volume: 3 Issue: 2, 99 - 104, 31.12.2016
Ahmet Daşdemir
Abstract
In this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are investigated. Moreover, certain sum formula consisting of the terms of the generalized Jacobsthal p-sequence are given
References
1. Stakhov AP. A generalization of the Fibonacci Q-matrix. National Academy of Sciences of Ukraine 9 (1999) 46-49.
2. Stakhov AP, Rozin B. Theory of Binet formulas for Fibonacci and Lucas p-numbers. Chaos Solitions and Fractals 27 (2006) 1162-1177.
3. Kilic E. The Binet formula, sum and representations of generalized Fibonacci p-numbers. European Journal of Combinatorics 29 (2008) 701-711.
4. Horadam AF. Jacobsthal Representation Numbers. Fibonacci Quarterly 34 (1996) 40-54.
5. Cerin Z. Sums of Squares and Products of Jacobsthal Numbers. Journal of Integer Sequences 10 (2007) Article 07.2.5.
6. Chen WYC, Louck JD. The combinatorial power of the companion matrix. Linear Algebra and its Applications 232 (1996) 261-78.
7. Koken F, Dozkurt D. On the Jacobsthal Numbers by Matrix Methods. International Journal of Contemporary Mathematical Sciences 3(13) (2008) 605-614.
There are 7 citations in total.
Details
Primary Language
English
Journal Section
Research Article
Authors
Ahmet Daşdemir
This is me
Kastamonu University, Department of Mathematics, Kastamonu, TURKEY
Publication Date
December 31, 2016
Published in Issue
Year 2016
Volume: 3 Issue: 2
Cite
Vancouver
Daşdemir A. The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence. Hittite J Sci Eng. 2016;3(2):99-104.