Some interpretations of the ( k , p ) -Fibonacci numbers

Natalia Paja; Iwona Włoch

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 3, page 297-307
  • ISSN: 0010-2628

Abstract

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In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the ( k , p ) -Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the ( k , p ) -Fibonacci numbers.

How to cite

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Paja, Natalia, and Włoch, Iwona. "Some interpretations of the $(k,p)$-Fibonacci numbers." Commentationes Mathematicae Universitatis Carolinae 62.3 (2021): 297-307. <http://eudml.org/doc/297597>.

@article{Paja2021,
abstract = {In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the $(k,p)$-Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the $(k,p)$-Fibonacci numbers.},
author = {Paja, Natalia, Włoch, Iwona},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fibonacci number; Pell number; tiling},
language = {eng},
number = {3},
pages = {297-307},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some interpretations of the $(k,p)$-Fibonacci numbers},
url = {http://eudml.org/doc/297597},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Paja, Natalia
AU - Włoch, Iwona
TI - Some interpretations of the $(k,p)$-Fibonacci numbers
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 3
SP - 297
EP - 307
AB - In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the $(k,p)$-Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the $(k,p)$-Fibonacci numbers.
LA - eng
KW - Fibonacci number; Pell number; tiling
UR - http://eudml.org/doc/297597
ER -

References

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  12. Kwaśnik M., Włoch I., The total number of generalized stable sets and kernels of graphs, Ars Combin. 55 (2000), 139–146. 
  13. Marques D., Trojovský P., On characteristic polynomial of higher order generalized Jacobsthal numbers, Adv. Difference Equ. (2019), Paper No. 392, 9 pages. 
  14. Miles E. P., Jr., 10.1080/00029890.1960.11989593, Amer. Math. Monthly 67 (1960), 745–752. DOI10.1080/00029890.1960.11989593
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