IJPAM: Volume 107, No. 4 (2016)

A RECURRENCE RELATION WITH
COMBINATORIAL IDENTITIES

George Grossman$^1$, Aklilu Zeleke$^2$, Xinyun Zhu$^3$, Tomas Zdrahal$^4$
$^1$Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48859, USA
$^2$Lyman Briggs College and Department of Statistics and Probability
Michigan State University
East Lansing, MI 48824, USA
$^3$Department of Mathematics
University of Texas of the Permian Basin
Odessa, TX 79762, USA
$^4$Katedra matematiky
Palacký University
Olomouc, CZECH REPUBLIC


Abstract. In the present paper, we consider a pair of recurrence relations whose simultaneous solution involves two parameters $k,n$. We also find generating function of the sequence. Identities related to the Fibonacci and Lucas numbers are given.

Received: September 25, 2015

AMS Subject Classification: 65Q30, 05A19, 11B39

Key Words and Phrases: recurrence relations, combinatorial identities, Fibonacci and Lucas numbers

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DOI: 10.12732/ijpam.v107i4.11 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 4
Pages: 939 - 948


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