Now showing items 1-10 of 62
The Matrix of Super Patalan Numbers and its Factorizations
(University of Nis, 2017)
Matrices related to Patalan and super-Patalan numbers are factored according to the LU-decomposition. Results are obtained via inspired guessings and later proved using methods from Computer Algebra.
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 ...
Identities with squares of binomial coefficients: An elementary and explicit approach
(Mathematical Institute of the Serbian Academy of Sciences and Arts, 2016)
In 2014, Slavik presented a recursive method to find closed forms for two kinds of sums involving squares of binomial coefficients. We give an elementary and explicit approach to compute these two kinds of sums. It is based ...
Various Sums Including the Generalized Fibonacci and Lucas numbers
(Palestine Polytechnic University,, 2015-09)
We compute certain sums including generalized Fibonacci and Lucas numbers as well as their alternating analogous. We show that these sums could be expressed by the terms of the sequences. Similar directions are given for ...
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.
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  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 ...
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.