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Now showing items 1-20 of 71

#### 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

(2016-09)

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 ...

#### 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 ...

#### 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.

#### The generalized Lilbert matrix

(Springer, 2016-09)

We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the ...

#### Evaluation of sums containing triple aerated generalized Fibonomial coefficients

(De Gruyter Open Ltd, 2017-04)

We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ...

#### The generalized reciprocal super Catalan matrix

(Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2016)

The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the LU-decomposition and their inverses, as well as the Cholesky ...

#### 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 ...

#### Decompositions of the Cauchy and Ferrers-Jackson polynomials

(Udruga Matematicara Osijek, 2016)

Recently, Witula and Slota have given decompositions of the Cauchy and Ferrers-Jackson polynomials [Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence ...

#### Some weighted sums of products of Lucas sequences

(Integers, 2013-11)

In this paper, we consider the weighted sums of products of Lucas sequences of the form (Formula Presented) where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using ...

#### 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 ...

#### Ruehr's identities with two additional parameters

(Integers, 2016-03)

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 ...

#### 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 ...

#### 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.

#### A class of non-symmetric band determinants with the Gaussian q-binomialcoefficients

(Taylor and Francis Ltd., 2017)

A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper ...

#### On sums of squares of Fibonomial coefficients by q-calculus

(World Scientific Publishing Co. Pte Ltd, 2016-09)

We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and ...

#### Generalized double binomial sums families by generating functions

(Utilitas Mathematica Publishing Inc., 2017-09)

We consider various double binomial sums related with certain second, third and fourth order recursions. Moreover a new binomial sums with complex coefficients related with a generalized second order recursion is derived. ...