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On binomial triple sums involving Fibonacci and Lucas numbers. (English) Zbl 1478.11020

Summary: In this paper, we consider interesting binomial and alternating binomial triple sums evaluated in multiplication forms in terms of the Fibonacci and Lucas numbers.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B65 Binomial coefficients; factorials; \(q\)-identities
05A10 Factorials, binomial coefficients, combinatorial functions
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References:

[1] E. Kilic and F. Tasdemir, On binomial double sums with Fibonacci and Lucas Numbers-I, Ars Combin., 144 (2019), 173-185. · Zbl 1463.11039
[2] E. Kilic and F. Tasdemir, On binomial double sums with Fibonacci and Lucas Numbers-II, Ars Combin., 144 (2019), 345-354. · Zbl 1449.11031
[3] E. Kilic, N. Omur, and Y. T. Ulutas, Alternating sums of the powers of Fibonacci and Lucas numbers, Miskolc Math. Notes, 12(1) (2011), 87-103. · Zbl 1240.11034 · doi:10.18514/MMN.2011.280
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