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Year 2016, Volume 3, Issue 2, 99 - 104, 31.12.2016
https://doi.org/10.17350/HJSE19030000038

Abstract

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
https://doi.org/10.17350/HJSE19030000038

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.

Details

Primary Language English
Journal Section Research Article
Authors

Ahmet DAŞDEMİR This is me
Kastamonu University, Department of Mathematics, Kastamonu, TURKEY

Publication Date December 31, 2016
Application Date
Acceptance Date
Published in Issue Year 2016, Volume 3, Issue 2

Cite

Bibtex @ { hjse860021, journal = {Hittite Journal of Science and Engineering}, eissn = {2148-4171}, address = {Hitit Üniversitesi Mühendislik Fakültesi Kuzey Kampüsü Çevre Yolu Bulvarı 19030 Çorum / TÜRKİYE}, publisher = {Hitit University}, year = {2016}, volume = {3}, number = {2}, pages = {99 - 104}, doi = {10.17350/HJSE19030000038}, title = {The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence}, key = {cite}, author = {Daşdemir, Ahmet} }
APA Daşdemir, A. (2016). The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence . Hittite Journal of Science and Engineering , 3 (2) , 99-104 . DOI: 10.17350/HJSE19030000038
MLA Daşdemir, A. "The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence" . Hittite Journal of Science and Engineering 3 (2016 ): 99-104 <https://dergipark.org.tr/en/pub/hjse/issue/59669/860021>
Chicago Daşdemir, A. "The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence". Hittite Journal of Science and Engineering 3 (2016 ): 99-104
RIS TY - JOUR T1 - The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence AU - AhmetDaşdemir Y1 - 2016 PY - 2016 N1 - doi: 10.17350/HJSE19030000038 DO - 10.17350/HJSE19030000038 T2 - Hittite Journal of Science and Engineering JF - Journal JO - JOR SP - 99 EP - 104 VL - 3 IS - 2 SN - -2148-4171 M3 - doi: 10.17350/HJSE19030000038 UR - https://doi.org/10.17350/HJSE19030000038 Y2 - 2022 ER -
EndNote %0 Hittite Journal of Science and Engineering The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence %A Ahmet Daşdemir %T The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence %D 2016 %J Hittite Journal of Science and Engineering %P -2148-4171 %V 3 %N 2 %R doi: 10.17350/HJSE19030000038 %U 10.17350/HJSE19030000038
ISNAD Daşdemir, Ahmet . "The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence". Hittite Journal of Science and Engineering 3 / 2 (December 2016): 99-104 . https://doi.org/10.17350/HJSE19030000038
AMA Daşdemir A. The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence. Hittite J Sci Eng. 2016; 3(2): 99-104.
Vancouver Daşdemir A. The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence. Hittite Journal of Science and Engineering. 2016; 3(2): 99-104.
IEEE A. Daşdemir , "The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence", Hittite Journal of Science and Engineering, vol. 3, no. 2, pp. 99-104, Dec. 2016, doi:10.17350/HJSE19030000038