We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
@article{bwmeta1.element.doi-10_2478_s11533-011-0089-9,
author = {Sergio Falcon},
title = {The k-Fibonacci matrix and the Pascal matrix},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1403-1410},
zbl = {1285.11055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0089-9}
}
Sergio Falcon. The k-Fibonacci matrix and the Pascal matrix. Open Mathematics, Tome 9 (2011) pp. 1403-1410. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0089-9/
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