Now showing items 1-10 of 70
On Fibonomial sums identities with special sign functions: analytically q-calculus approach
(De Gruyter Open Ltd, 2018-06-26)
Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809-818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. ...
Evaluation of various partial sums of Gaussian q-binomial sums
(Springer Berlin Heidelberg, 2018-06-01)
We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe's formula and a q-version of the celebrated algorithm of Zeilberger. ...
Three binomial sums weighted by falling and rising factorials
In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial ...
Double binomial sums and double sums related with certain linear recurrences of various order
(Chiang Mai University, 2018-05-01)
In this paper, we derive new double binomial sums families related with generalized second, third and certain higher order linear recurrences. We also present various parametric generalizations of some results of [1, 2]. ...
A Wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns
(Bulgarian Acad Science, 2017)
In this paper, we make a contribution to the enumeration of permutations avoiding a quadruples of 4-letter patterns by establishing a Wilf class composed of 19 symmetry classes.
Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions
(World Scientific Publishing Co. Pte Ltd, 2016-03)
We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ...
Sylvester-Tridiagonal Matrix with Alternating main diagonal entries and its Spectra
(Walter De Gruyter Gmbh, 2013-11)
Recently some generalizations of Sylvester type tridiagonal matrices have been considered with their spectra. We introduce a new kind generalization of Sylvester type tridiagonal matrix by considering its main diagonal entries. ...
On Alternating Weighted Binomıal Sums With Falling Factorıals
(Int Center Scientific Research & Studies, 2017)
In this paper, by inspiring from earlier recent works on weighted binomial sums, we introduce and compute new kinds of binomial sums including rising factorial of the summation indices.
Closed Form Evaluation Of Melham's Reciprocal Sums
(Univ Miskolc Inst Math, 2017)
Recently Melham  gives closed formul ae for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we ...
Two Variants of the Reciprocal Super Catalan Matrix
(Kyungpook National University, 2016-06)
In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.