Now showing items 1-10 of 75
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. ...
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]. ...
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 ...
An analytical approach: Explicit inverses of periodic tridiagonal matrices
(Elsevier B. V., 2018-06-01)
We derive an explicit formula for the inverse of a general, periodic, tridiagonal matrix. Our approach is to derive its LU factorization using backward continued fractions (BCF) which are an essential tool in number theory. ...
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 ...
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 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 ...
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 ...