New combinatorial proof of the multiple binomial coefficient identity
Abstract
Introduction/purpose: In this paper a new combinatorial proof of an already existing multiple sum with multiple binomial coefficients is given. The derived identity is related to the Fibonacci numbers.
Methods: Combinatorial reasoning is used to obtain the results.
Results: The already known identity was obtained by using a new combinatorial reasoning.
Conclusions: The new combinatorial reasoning led to the solution of the already existing identity.
References
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Gessel, I. 1972. Fibonacci is a Square. The Fibonacci Quarterly, 10(4), pp.417–419 [online]. Available at: https://www.fq.math.ca/Issues/10-4.pdf [Accessed: 18 March 2022].
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