Naslov
Bijective Proof of Extensions of the Sury’s Identity

Autori
Martinjak, Ivica

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Combinatorial and Additive Number Theory / - , 2016

Skup
Combinatorial and Additive Number Theory 2016

Mjesto i datum
Graz, Austrija, 04.01.2016. - 08.01.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Fibonacci sequence ; Sury identity ; tilings

Sažetak
We present two families of Fibonacci-Lucas identities, with the {; ; \it Sury's identity}; ; $\sum_{; ; k=0}; ; ^n 2^k L_k = 2^{; ; n+1 }; ; F_{; ; n+1}; ; $ being the best known representative of one of the family. While these results can be proved by means of the basic identity relating Fibonacci and Lucas sequences we also provide a combinatorial proof. Our bijective proof is based on the known fact that the product $m^n f_n$, where $f_n=F_{; ; n+1}; ; $, represents the number of {; ; \it colored $n$-board tilings}; ; with {; ; \it squares}; ; in $m$ colors and {; ; \it dominoes}; ; in $m^2$ colors.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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