Related papers: A formula for constructing Mignotte sequences
Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives an explicit formula for Bernoulli numbers of even index. The formula contains a remarkable sequence of determinants.
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
We find an explicit formula for the generating function for the squaring the terms of an $\ell^{th}$ order linear recurrence.
We are interested in formulas for the number of elements in certain classes of numerical semigroups
A simple way is shown to construct the length $\pi$ from the unit length with 4 digits accuracy.
We give a twining character formula for Demazure modules.
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
We propose several procedures for creating new families of integer sequences based on the method of Cantor diagonalization. Then we modify and generalize this method. The paper includes explicit formulas for most proposed families of…
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low…
We consider the problem of constructing semisimple subalgebras of real (semi-) simple Lie algebras. We develop computational methods that help to deal with this problem. Our methods boil down to solving a set of polynomial equations. In…
A formula to construct classic exact solutions to Tricomi partial differential equation. The steps to obtain this formula require only elementary resolution of a simple system of first order PDEs.
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
Simple formulas are given for generating Chern-Simons basic invariant polynomials by repeated exterior differentiation for n-dimensional differentiable manifolds having a general linear connection.
The paper provides a necessary and sufficient condition for the composition of multivariable formal power series and present the Generalized Chain Rule for formal power series of multiple variables.
In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…
This study applies the binomial, k-binomial, rising k-binomial and falling k-binomial transforms to the modified k-Fibonacci-like sequence. Also, the Binet formulas and generating functions of the above mentioned four transforms are newly…
We extend Hoste-Shanahan's calculations for the A-polynomial of twist knots, to give an explicit formula.