Abstract
In this paper, we consider Pell numbers. We define the gell numbers which generalize the Pell numbers. Moreover, we derive Binet-like formula,
generating function and exponential generating function for the gell sequence. Also, we obtain the gell series and some important identities for the
gell sequence.
Keywords
Pell sequence generalized Pell sequence Binet-like formula generating function exponential generating function
References
- F. T. Aydin and K. Köklü, On Generalizations of the Pell Sequence. arXiv preprint arXiv:1711.06260 (2017).
- M. Bicknell, A primer on the Pell sequence and related sequences; Fibonacci Quarterly, 13(4), 345-349 (1975).
- A. F. Horadam, Pell Identities, The Fibonacci Quarterly, 9 (3), 245-252 (1971).
- T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer-Verlag New York, 2014.
- T. Koshy, Fibonacci and Lucas Numbers with Applications Volume 1, John Wiley Sons, New Jersey, 2018.
- R. Melham, Sums involving Fibonacci and Pell numbers, Portugal. Math., 56 (3), 309-317 (1999).
Abstract
References
- F. T. Aydin and K. Köklü, On Generalizations of the Pell Sequence. arXiv preprint arXiv:1711.06260 (2017).
- M. Bicknell, A primer on the Pell sequence and related sequences; Fibonacci Quarterly, 13(4), 345-349 (1975).
- A. F. Horadam, Pell Identities, The Fibonacci Quarterly, 9 (3), 245-252 (1971).
- T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer-Verlag New York, 2014.
- T. Koshy, Fibonacci and Lucas Numbers with Applications Volume 1, John Wiley Sons, New Jersey, 2018.
- R. Melham, Sums involving Fibonacci and Pell numbers, Portugal. Math., 56 (3), 309-317 (1999).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Submission Date | January 24, 2020 |
| Acceptance Date | March 2, 2020 |
| Publication Date | January 31, 2020 |
| Published in Issue | Year 2020 Volume: 3 Issue: 1 |