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. ...

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.

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 ...

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. ...

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.

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 ...

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.

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 ...

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.

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 ...

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 ...

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 ...

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 ...

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 ...

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. ...

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.

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 ...

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 ...

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 ...

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.