Results 51 to 60 of about 1,693 (108)
Gaussian Generalized Tetranacci Numbers [PDF]
, 2019 In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.
arxiv +1 more source
, 2013 We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the first kind, and we also introduce a skyscraper sequence.Comment: 7 pages, 1 ...
Khovanova, Tanya, Lewis, Joel Brewster
core
A new approach to the r-Whitney numbers by using combinatorial differential calculus
Acta Universitatis Sapientiae: Mathematica, 2019 In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}.
Méndez Miguel A., Ramírez José L.
doaj +1 more source
On Cauchy Products of q−Central Delannoy Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this study, we have examined q− central Delannoy numbers and their Cauchy products. We have given some related equalities using the properties of recurrence relations.
Halıcı Serpil
doaj +1 more source
Logarithmically complete monotonicity of a function related to the Catalan-Qi function
Acta Universitatis Sapientiae: Mathematica, 2016 In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.
Qi Feng, Guo Bai -Ni
doaj +1 more source
Arithmetic and Geometric Progressions in Productsets over Finite Fields
, 2007 Given two sets $\cA, \cB \subseteq \F_q$ of elements of the finite field $\F_q$ of $q$ elements, we show that the productset $$ \cA\cB = \{ab | a \in \cA, b \in\cB\} $$ contains an arithmetic progression of length $k \ge 3$ provided that ...
Shparlinski, Igor E.
core +1 more source
Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequences [PDF]
arXiv, 2019 We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships between the moments of these orthogonal polynomials, the moments of the defining Laurent biorthogonal polynomials, and the expansions of $T$-fractions. Closed form expressions
arxiv
Bernoulli type polynomials on Umbral Algebra
, 2011 The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we
G Bretti +8 more
core +1 more source
A note on number triangles that are almost their own production matrix [PDF]
arXiv, 2018 We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these triangles relate to sequences that have interesting convolution recurrences and continued fraction generating functions.
arxiv
Modular forms, hypergeometric functions and congruences
, 2013 Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that ...
Kazalicki, M.
core +2 more sources