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Year 2021, , 63 - 67, 30.06.2021
https://doi.org/10.47000/tjmcs.835237

Abstract

References

  • [1] Aydın, F. G., Köklü, K., Yüce, S., Generalized Dual Pell Quaternions, Notes on Number Theory and Discrete Mathematics, 23(4), (2017), 66–84.
  • [2] Bicknell, M., Hoggatt, V. E., A primer for the Fibonacci Numbers, Santa Clara, Calif.: The Fibonacci Association, B-10(1972), 45.
  • [3] Bruce, I., A Modified Tribonacci Sequence, The Fibonacci Quarterly 22, 3(1984), 244–246.
  • [4] Ercolano, J., Matrix generators of Pell sequences, The Fibonacci Quarterly, 17 (1)(1979), 71–77.
  • [5] Horadam, A. F., Pell identities, The Fibonacci Quarterly 26, 9 (3)(1971), 245–252.
  • [6] Kılıç, E., Taşcı, D., The generalized Binet formula, representation and sums of the generalized order- Pell numbers, Taiwanese J. Math., 10 (6)(2006), 1661–1670.
  • [7] Kılıç, E., The generalized order- k Fibonacci - Pell sequence by matrix methods, Journal of Computational and Applied Mathematics, 209(2)(2007), 133–145.
  • [8] Pethö, A., The Pell sequence contains only trivial perfect powers, In Colloquia on Sets, Graphs and Numbers, Soc. Math., J´anos Bolyai, North-Holland, Amsterdam (1991), 561–568.
  • [9] Pin-Yen, L., De Moivre-Type Identities for the Tribonacci Numbers, The Fibonacci Quarterly, 2(1988), 131–134.
  • [10] Pin-Yen, L., De Moivre-Type Identities for the Tetranacci Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht(1991), https://doi.org/10.1007/978-94-011-3586-324.
  • [11] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/.
  • [12] Soykan, Y., On Generalized third-order Pell numbers, Asian Journal of Advanced Research and Reports, 6(1)(2019), https://doi.org/10.9734/ajarr/2019/v6i130144, 1–18.

De Moivre-Type Identities for the Pell Numbers

Year 2021, , 63 - 67, 30.06.2021
https://doi.org/10.47000/tjmcs.835237

Abstract

This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers. Moreover, we obtain the De Moivre-type identities for these numbers. In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.

References

  • [1] Aydın, F. G., Köklü, K., Yüce, S., Generalized Dual Pell Quaternions, Notes on Number Theory and Discrete Mathematics, 23(4), (2017), 66–84.
  • [2] Bicknell, M., Hoggatt, V. E., A primer for the Fibonacci Numbers, Santa Clara, Calif.: The Fibonacci Association, B-10(1972), 45.
  • [3] Bruce, I., A Modified Tribonacci Sequence, The Fibonacci Quarterly 22, 3(1984), 244–246.
  • [4] Ercolano, J., Matrix generators of Pell sequences, The Fibonacci Quarterly, 17 (1)(1979), 71–77.
  • [5] Horadam, A. F., Pell identities, The Fibonacci Quarterly 26, 9 (3)(1971), 245–252.
  • [6] Kılıç, E., Taşcı, D., The generalized Binet formula, representation and sums of the generalized order- Pell numbers, Taiwanese J. Math., 10 (6)(2006), 1661–1670.
  • [7] Kılıç, E., The generalized order- k Fibonacci - Pell sequence by matrix methods, Journal of Computational and Applied Mathematics, 209(2)(2007), 133–145.
  • [8] Pethö, A., The Pell sequence contains only trivial perfect powers, In Colloquia on Sets, Graphs and Numbers, Soc. Math., J´anos Bolyai, North-Holland, Amsterdam (1991), 561–568.
  • [9] Pin-Yen, L., De Moivre-Type Identities for the Tribonacci Numbers, The Fibonacci Quarterly, 2(1988), 131–134.
  • [10] Pin-Yen, L., De Moivre-Type Identities for the Tetranacci Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht(1991), https://doi.org/10.1007/978-94-011-3586-324.
  • [11] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/.
  • [12] Soykan, Y., On Generalized third-order Pell numbers, Asian Journal of Advanced Research and Reports, 6(1)(2019), https://doi.org/10.9734/ajarr/2019/v6i130144, 1–18.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Seda Yamaç Akbıyık 0000-0003-1797-674X

Mücahit Akbıyık 0000-0002-0256-1472

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Yamaç Akbıyık, S., & Akbıyık, M. (2021). De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science, 13(1), 63-67. https://doi.org/10.47000/tjmcs.835237
AMA Yamaç Akbıyık S, Akbıyık M. De Moivre-Type Identities for the Pell Numbers. TJMCS. June 2021;13(1):63-67. doi:10.47000/tjmcs.835237
Chicago Yamaç Akbıyık, Seda, and Mücahit Akbıyık. “De Moivre-Type Identities for the Pell Numbers”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 63-67. https://doi.org/10.47000/tjmcs.835237.
EndNote Yamaç Akbıyık S, Akbıyık M (June 1, 2021) De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science 13 1 63–67.
IEEE S. Yamaç Akbıyık and M. Akbıyık, “De Moivre-Type Identities for the Pell Numbers”, TJMCS, vol. 13, no. 1, pp. 63–67, 2021, doi: 10.47000/tjmcs.835237.
ISNAD Yamaç Akbıyık, Seda - Akbıyık, Mücahit. “De Moivre-Type Identities for the Pell Numbers”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 63-67. https://doi.org/10.47000/tjmcs.835237.
JAMA Yamaç Akbıyık S, Akbıyık M. De Moivre-Type Identities for the Pell Numbers. TJMCS. 2021;13:63–67.
MLA Yamaç Akbıyık, Seda and Mücahit Akbıyık. “De Moivre-Type Identities for the Pell Numbers”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 63-67, doi:10.47000/tjmcs.835237.
Vancouver Yamaç Akbıyık S, Akbıyık M. De Moivre-Type Identities for the Pell Numbers. TJMCS. 2021;13(1):63-7.