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Keywords:
Fibonacci number; Pell number; tiling
Fibonacci number; Pell number; tiling
Summary:
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.
References:
[1] Bednarz N.: On $(k,p)$-Fibonacci numbers. Mathematics 9 (2021), no. 7, page 727. DOI 10.3390/math9070727
[2] Bednarz N., Włoch A., Włoch I.: The Fibonacci numbers in edge coloured unicyclic graphs. Util. Math. 106 (2018), 39–49.
[3] Bednarz U., Bród D., Szynal-Liana A., Włoch I., Wołowiec-Musiał M.: On Fibonacci numbers in edge coloured trees. Opuscula Math. 37 (2017), no. 4, 479–490. DOI 10.7494/OpMath.2017.37.4.479
[4] Bednarz U., Włoch I.: Fibonacci and telephone numbers in extremal trees. Discuss. Math. Graph Theory 38 (2018), no. 1, 121–133. DOI 10.7151/dmgt.1997
[5] Bednarz U., Włoch I., Wołowiec-Musiał M.: Total graph interpretation of the numbers of the Fibonacci type. J. Appl. Math. (2015), Art. ID 837917, 7 pages.
[6] Berge C.: Principles of Combinatorics. translated from the French Mathematics in Science and Engineering, 72, Academic Press, New York, 1971.
[7] Catarino P.: On some identities and generating functions for $k$-Pell numbers. Int. J. Math. Anal. (Ruse) 7(2013), no. 37–40, 1877–1884. DOI 10.12988/ijma.2013.35131
[8] Diestel R.: Graph Theory. Graduate Texts in Mathematics, 173, Springer, Berlin, 2005. Zbl 1218.05001
[9] Falcón S., Plaza Á.: On the Fibonacci $k$-numbers. Chaos Solitons Fractals 32 (2007), no. 5, 1615–1624. DOI 10.1016/j.chaos.2006.09.022
[10] Kiliç E.: The generalized Pell $(p, i)$-numbers and their Binet formulas, combinatorial representations, sums. Chaos Solitons Fractals 40 (2009), no. 4, 2047–2063. DOI 10.1016/j.chaos.2007.09.081
[11] Koshy T.: Pell and Pell-Lucas Numbers with Applications. Springer, New York, 2014.
[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.: Generalized Fibonacci numbers and associated matrices. Amer. Math. Monthly 67 (1960), 745–752. DOI 10.1080/00029890.1960.11989593
[15] Stakhov A. P.: An Introduction to the Algorithmic Theory of Measurement. Sovetskoe Radio, Moscow, 1977 (Russian).
[16] Prodinger H., Tichy R. F.: Fibonacci numbers of graphs. Fibonacci Quart. 20 (1982), no. 1, 16–21.
[17] Włoch I.: On generalized Pell numbers and their graph representations. Comment. Math. 48 (2008), no. 2, 169–175.
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