Now showing items 1-6 of 6
A curious matrix-sum identity and certain finite sums identities
(World Scientific Publishing Co. Pte Ltd, 2015-09)
In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary ...
Generalized Binomial Convolution Of The Mth Powers Of The Consecutive Integers With The General Fibonacci Sequence
(De Gruyter Open Ltd, 2016-12)
In this paper, we consider Gauthier's generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.
Various Sums Including the Generalized Fibonacci and Lucas numbers
(Palestine Polytechnic University,, 2015-09)
We compute certain sums including generalized Fibonacci and Lucas numbers as well as their alternating analogous. We show that these sums could be expressed by the terms of the sequences. Similar directions are given for ...
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.
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 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 ...