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Combinatorial Sums of Generalized Fibonacci and Lucas Numbers
(CHARLES BABBAGE RES CTR, 2011) Uslu, K.; Taskara, N.; Gulec, H. H.
In this study, we consider generalization of the well-known Fibonacci and Lucas numbers related with combinatorial sums by using finite differences. To write generalized Fibonacci and Lucas sequences in a new direct way, we investigate some new properties of these numbers.
A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients
(ELSEVIER SCIENCE INC, 2013) Gulec, H. H.; Taskara, N.; Uslu, K.
In this study, Fibonacci and Lucas numbers have been obtained by using generalized Fibonacci numbers. In addition, some new properties of generalized Fibonacci numbers with binomial coefficients have been investigated to write generalized Fibonacci sequences in a new direct way. Furthermore, it has been given a new formula for some Lucas numbers. (C) 2013 Elsevier Inc. All rights reserved.