In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo m.
@article{bwmeta1.element.doi-10_1515_math-2016-0100,
author = {Inci G\"ultekin and \"Om\"ur Deveci},
title = {On the arrowhead-Fibonacci numbers},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {1104-1113},
zbl = {06675361},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0100}
}
Inci Gültekin; Ömür Deveci. On the arrowhead-Fibonacci numbers. Open Mathematics, Tome 14 (2016) pp. 1104-1113. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0100/