On some new sums of Fibonomial coefficients
type: Item
instance of: scholarly article
zbMATH Open document ID: 1293.11031
author: Diego Marques
author: Pavel Trojovský
publication date: 2012-06-29T00:00:00Z
full work available at URL: marques2.pdf
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 6051050
MaRDI profile type: Publication
title: On some new sums of Fibonomial coefficients
published in: The Fibonacci Quarterly
review text: Let \(F_n\) be the \(n\)th Fibonacci number. The Fibonomial coefficients \({n\brack k}_F\) are defined for \(n\geq k > 0\) as follows NEWLINE\[NEWLINE{n\brack k}_F = \frac{F_nF_{n-1}\cdots F_{n -k+1}}{F_1F_2\cdots F_k}NEWLINE\]NEWLINE with \({n\brack 0}_F= 1\) and \({n\brack 0}_F= 0\) for \(n < k\). In this paper, the authors find some interesting sums among Fibonomial coefficients. In particular, they prove that NEWLINE\[NEWLINE\sum_{j=0}^{4m+2} (-1)^{\frac j2 (j+1)} {4m+2\brack j}_F F_{n+4m+2-j} = 0,NEWLINE\]NEWLINE is valid for all non-negative integers \(m\) and \(n\).
reviewed by: Olaf Ninnemann
description: scientific article; zbMATH DE number 6051050