Affiliation:
1. The Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
Abstract
In this paper, we study the Oresme hybrationals that generalize Oresme hybrid numbers and Oresme rational functions. We give a reccurence relation and a generating function for Oresme hybrationals. Moreover, we give some of their properties, among others, Binet formulas and general bilinear index-reduction formulas, through which we can obtain Catalan-, Cassini-, Vajda-, and d’Ocagne-type identities.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference20 articles.
1. Counting paths in corridors using circular Pascal arrays;Ault;Discrete Math.,2014
2. On Integer-Sequence-Based Constructions of Generalized Pascal Triangles;Barry;J. Integer Seq.,2006
3. Some geometry of Pascal’s triangle;Kicey;Pi Mu Epsilon J.,2011
4. Morphic words, Beatty sequences and integer images of the Fibonacci language;Dekking;Theoret. Comput. Sci.,2020
5. The sum of digits functions of the Zeckendorf and the base phi expansions;Dekking;Theor. Comput. Sci.,2021