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New Identities from a Combinatorial Approach to Generalized Fibonacci and Generalized Lucas Numbers

We present here some new identities for generalizations of Fibonacci and Lucas numbers by combinatorially interpreting these numbers in terms of numbers of certain tilings of a $1 \times m$ board. As a consequence, some new interesting identities involving the ordinaries Fibonacci and Lucas numbers are derived.

preprint2016arXivOpen access
Robson da Silva
math.CO
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Robson da Silva

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