Now showing items 1-10 of 70
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 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.
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 ...
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 ...
Ruehr's identities with two additional parameters
We present generalizations of Ruehr’s identities with two additional parameters. We prove the claimed results by two di?erent proof methods, namely combinatorially and mechanically. Further, we derive recurrence relations ...
Evaluation of sums involving products of Gaussian q-binomial coefficients with applications to Fibonomial sums
(Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2017)
Sums of products of two Gaussian q-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting ...
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.