Ömür, Neşe; Duran, Ömer On binomial triple sums involving Fibonacci and Lucas numbers. (English) Zbl 1478.11020 Honam Math. J. 42, No. 1, 49-62 (2020). 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. Cited in 1 Document MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B65 Binomial coefficients; factorials; \(q\)-identities 05A10 Factorials, binomial coefficients, combinatorial functions Keywords:binomial triple sums; closed formula; Fibonacci and Lucas numbers PDFBibTeX XMLCite \textit{N. Ömür} and \textit{Ö. Duran}, Honam Math. J. 42, No. 1, 49--62 (2020; Zbl 1478.11020) Full Text: DOI 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 [4] M. Khan and H. Kwong, Some binomial identities associated with the generalized natural number sequence, The Fibonacci Quarterly, 49(1) (2011), 57-65. · Zbl 1219.11027 [5] H. Prodinger, On a sum of Melham and its variants, The Fibonacci Quarterly, 46-47(3) (2008-2009), 207-215. · Zbl 1220.11023 [6] M. Wiemann and C. Cooper, Divisibility of an F-L type convolution, Applications of Fibonacci Numbers, 9 (2004), 267-287. · Zbl 1066.11008 [7] S. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.