On Some Multinomial Sums Related to the Fibonacci Type Numbers-Reference-Cited by-同舟云学术

On Some Multinomial Sums Related to the Fibonacci Type Numbers

Published:2020-12-01 Issue:1 Volume:77 Page:99-108
ISSN:1210-3195
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Włoch Iwona¹,Włoch Andrzej²

Affiliation:

1. Department of Discrete Mathematics , Rzeszow University of Technology , Rzeszow , Poland

2. Department of Mathematical Modeling , Rzeszow University of Technology , Rzeszow , Poland

Abstract

Abstract In this paper we investigate Fibonacci type sequences defined by kth order linear recurrence. Based on their companion matrix and its graph interpretation we determine multinomial and binomial formulas for these sequences. Moreover we present a graphical rule for calculating the words of these sequences from the Pascal’s triangle.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2020-0035

Reference10 articles.

1. [1] BEDNARZ, U.—W LOCH, I.—WO LOWIEC-MUSIA L, M.: Total graph interpretation of the number of the Fibonacci type, J. Appl. Math. (2015), Article ID 837917, 7 pp.

2. [2] ER, M. C.: Sums of Fibonacci numbers by matrix methods, Fibonacci Quart. 22 (1984), no. 3, 204–207.

3. [3] FALCÓN SANTANA, S.—DÍAZ-BARRERO, J. L.: Some properties of sums involving Pell numbers. Missouri J. Math. Sci. 18 (2006), no. 1, 33–40.

4. [4] HORADAM, A. F.: Pell identities, Fibonacci Quart. 9 (1971), no. 3, 245–252, 263.

5. [5] D. KALMAN: Generalized Fibonacci numbers by matrix methods, Fibonacci Quart. 20 (1982), no. 1, 73–76.

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