Related papers: Recurrence for powers of recursive sequence II
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms…
Convolution powers of $1/x$ are transformed into functions $f_n$, which satisfy a simple recurrence relation. Solutions are characterized and analyzed.
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q>2). The procedure allows to prove that no such multiples exist in many instances.
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
The recursive relation starts to appear by putting a function $y(x)=\sum_{n=0}^{\infty }d_n x^n$ into a linear ordinary differential equation (ODE). There can be $d$-term of sequences in the recurrence relation of a power series where…
We define a triangular array closely related to Stern's diatomic array and show that for a fixed integer $r\geq 1$, the sum $u_r(n)$ of the $r$th powers of the entries in row $n$ satisfy a linear recurrence with constant coefficients. The…
In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since…
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We give estimates from below for the greatest prime factor of the n-th term of a binary recurrence sequence.