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Formulas for binomial sums including powers of fibonacci and lucas numbers
(Politechnica University of Bucharest, 2015)
Recently Prodinger  proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers.
Asymmetric generalizations of the Filbert matrix and variants
(Mathematical Institute of the Serbian Academy of Sciences and Arts, 2014)
Four generalizations of the Filbert matrix are considered; with additional asymmetric parameter settings. Explicit formula are derived for the LU-decompositions, their inverses, and the inverse matrix. The approach is ...
A generalization of a conjecture of Melham
(Utilitas Mathematica Publishing Inc., 2014-03)
A generalization of one of Melham's conjectures is presented. After writing it in terms of Gaussian q binomial coefficients, a solution is found using the elementary technique of partial fraction decomposition.
Sums of products of generalized Fibonacci and Lucas numbers
Sums of products of a fixed number of Fibonacci(-type) numbers can be computed automatically. This extends, at least in principle, various results about two factors that appeared in the literature. More general results ...
Some classes of alternating weighted binomial sums
In this paper, we consider three classes of generalized alternating weighted binomial sums of the form where f (n, i, k, t) will be chosen as UktiVkn?k(t+2)i, UktiVkn?kti and UtkiV(k+1)tn?(k+2)ti. We use the Binet formula ...
New Sums Identities In Weighted Catalan Triangle With The Powers Of Generalized Fibonacci And Lucas Numbers
(Charles Babbage Research Centre, 2014-07)
In this paper, we consider a generalized Catalan triangle defined by k(m)/n(2n n - k) for positive integer m. Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers ...
The generalized q-Pilbert matrix
(De Gruyter Open Ltd, 2014-10)
A generalized q-Pilbert matrix from[KILIC, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370-1377] is further generalized, introducing one additional parameter. Explicit formul' are derived for ...
A proof of a conjecture of Marques and Trojovsky
(University of Miskolc, 2014)
In this paper, we consider Marques and Trojovsky's conjecture involving Fibonomial coefficients, Fibonacci and Lucas numbers. After rewriting it in terms of Gaussian q-binomial coefficients and q-Pochhammer symbols, we ...
A variant of the reciprocal super Catalan matrix
(De Gruyter Open Ltd, 2015-01)
Recently Prodinger  considered the reciprocal super Catalan matrix and gave explicit formula for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues ...
Evaluation of Hessenberg Determinants via Generating Function Approach
(University of Nis, 2017)
In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ...