On Some New Sums of Fibonomial Coefficients

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F12%3A50000628" target="_blank" >RIV/62690094:18470/12:50000628 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On Some New Sums of Fibonomial Coefficients

Original language description

Let (Fn) be the Fibonacci sequence given by the recurrence relation F_{n+2}=F_{n+1}+F_n, with F_0=0 and F_1=1. The Fibonomial coefficients [m,k]_F, which are a generalization of binomial coefficients, arise by replacing the natural numbers by the terms of sequence (F_n). During the last decades several identities among these numbers have been found. For example Gould in 1969 derived the relation sum_j=k^n (F_j- F_{j-k})/F_k [j-1,k-1]_F = [n,k]_F and other interesting identities found Lind in 1971 and recently Kilic et al. derive a very general formula. In this paper, we shall provide some interesting sums. In particular, we prove that sum_j=0^n (-1)^{j/2(j+1)} [4m+2,j]_F F_{n+4m+2-j} = 0 holds for all non-negative integers m and n.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Fibonacci quarterly

ISSN

0015-0517

e-ISSN

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Volume of the periodical

50

Issue of the periodical within the volume

2

Country of publishing house

CA - CANADA

Number of pages

8

Pages from-to

155-162

UT code for WoS article

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EID of the result in the Scopus database

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