## Search

Now showing items 1-20 of 70

#### 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. ...

#### 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 [1] 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.

#### 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 ...

#### Some Subsequences of the Generalized Fibonacci and Lucas Sequences

(Utilitas Mathematica Publishing Inc., 2015-07)

We derive first-order nonlinear homogeneous recurrence relations for certain subsequences of generalized Fibonacci and Lucas sequences. We also present a polynomial representation for the terms of Lucas subsequence.

#### Variants of the Filbert Matrix

(Fibonacci Association, 2013-05)

A variation of the Filbert matrix from [1] is introduced, which has one additional Fibonacci factor in the numerator. We also introduce its Lucas counterpart by taking Lucas numbers instead of Fibonacci numbers in a similar ...

#### 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 ...

#### Some Gaussian binomial sum formulæ with applications

(Indian National Science Academy, 2016-09)

We introduce and compute some Gaussian q-binomial sums formul ae. In order to prove these sums, our approach is to use q-analysis, in particular a formula of Rothe, and computer algebra. We present some applications of our ...

#### 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. ...

#### Generalized binary recurrent quasi-cyclic matrices

(Eszterhazy Karoly College, 2014-11)

In this paper, we obtain solutions to infinite family of Pell equations of higher degree based on the more generalized Fibonacci and Lucas sequences as well as their all subsequences of the form {ukn} and {vkn} for odd k > 0.

#### 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 ...

#### 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 ...

#### 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.