Now showing items 1-10 of 20
The Matrix of Super Patalan Numbers and its Factorizations
(University of Nis, 2017)
Matrices related to Patalan and super-Patalan numbers are factored according to the LU-decomposition. Results are obtained via inspired guessings and later proved using methods from Computer Algebra.
Identities with squares of binomial coefficients: An elementary and explicit approach
(Mathematical Institute of the Serbian Academy of Sciences and Arts, 2016)
In 2014, Slavik presented a recursive method to find closed forms for two kinds of sums involving squares of binomial coefficients. We give an elementary and explicit approach to compute these two kinds of sums. It is based ...
Some Double binomial sums related to Fibonacci, Pell and generalized order-k Fibonacci numbers
(Rocky Mt Math Consortium, 2013-10)
We consider some double binomial sums related to the Fibonacci and Pell numbers and a multiple binomial sum related to the generalized order-k Fibonaccinumbers. The Lagrange-Burmann formula and other well-known techniques ...
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.
A note on the conjecture of Ramirez and Sirvent
(University of Waterloo, 2014-02)
We give a proof of a recent conjecture of Ramirez and Sirvent on the generating function of the incomplete Tribonacci 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 ...
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 ...
Formulæ related to the q-Dixon formula with applications to Fibonomial sums
(Kluwer Academic Publishers, 2015-06)
The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...
Closed form evaluation of restricted sums containing squares of Fibonomial coefficients
(Politechnica University of Bucharest, 2016)
We give a systematic approach to compute certain sums of squares Fibonomial coefficients with powers of generalized Fibonacci and Lucas numbers as coefficients; the range of the summation is not the natural one but about ...
Closed form evaluation of sums containing squares of Fibonomial coefficients
(De Gruyter Open Ltd, 2016-06)
We give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms ...