Triple sums including Fibonacci numbers with three binomial coefficients

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NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, vol.27, no.1, pp.188-197, 2021 (ESCI) identifier


In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.