The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence

Year 2016, , 99 - 104, 31.12.2016

Ahmet Daşdemir

https://doi.org/10.17350/HJSE19030000038

Cited By: 4

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

Keywords

Jacobsthal sequence, Generating Matrix, Binet Formula, Combinatorial representation.

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.