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A certain class of rank two pointed Hopf algebras is considered. The simple modules of their Drinfel'd double is described using Radford's method \cite{rad}. The socle of the tensor product of two such modules is computed and a formula…
We find an explicit formula for the generating function for the squaring the terms of an $\ell^{th}$ order linear recurrence.
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
The Tribonacci sequence is a well-known example of third order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Tribonacci sequence is introduced and defined by…
The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.
In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These…
In this paper we focus on finding all the factorials expressible as a product of a fixed number of $2k$-nacci numbers with $k \geq 2$. We derive the 2-adic valuation of the $2k$-nacci sequence and use it to establish bounds on the solutions…
We reprove a few results concerning paperfolding sequences using properties of Catalan numbers modulo 2.
We state and prove product formulae for several generating functions for sequences $(a_n)_{n\ge0}$ that are defined by the property that $Pa_n+b^2$ is a square, where $P$ and $b$ are given integers. In particular, we prove corresponding…
Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach,…
In this study, we investigate Horadam sequence as generalization of linear recurrence equations of order two. By the aid of this sequence we obtain a new generalization for sequences of dual quaternions and dual octonions. Moreover, we…
A "truncation" of Pascal's triangle is a triangular array of numbers that satisfies the usual Pascal recurrence but with a boundary condition that declares some terminal set of numbers along each row of the array to be zero. Presented here…
We establish a recursive relation for the bipartition number $p_2(n)$ which might be regarded as an analogue of Euler's recursive relation for the partition number $p(n)$. Two proofs of the main result are proved in this article. The first…
We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
Many important special numbers appear in the expansions of some polynomials in terms of central factorials and vice versa, for example central factorial numbers, degenerate central factorial numbers, and central Lah numbers which are…
Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many different ways. In addition, formulas and identities involving these…
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…
In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal…