Using a theorem of N. Chomsky and M. Schützenberger one can characterize sequences of integers which satisfy linear recurrence relations with constant coefficients (C-finite sequences) as differences of two sequences counting words in regular languages. We prove an analog for P-recursive (holonomic) sequences in terms of counting certain lattice paths.

This paper concerns a new type of approximant for series analysis. By incorporating linear recurrence techniques, such as are involved with second order di erential approximants, algebraic approximants can be extended to nonlinear di erential approximants. The discussion of nonlinearities is constrained by discussing approximants just one step removed from second order algebraic approximants. T...

We describe a methodology for mapping linear recurrence equations to a spectrum of systolic architectures. First, we design a systolic program in a very general architecture referred to as Basic Systolic Architecture and establish the correctness of the implementation. Next, we show how ef-cient transformations/implementations of programs for diierent systolic architectures can be obtained thro...

In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A sufficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and result...

We consider the higher-order nonlinear difference equation xn 1 p qxn−k / 1 xn rxn−k , n 0, 1, . . . with the parameters, and the initial conditions x−k, . . . , x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open probl...

We prove that for any base b ≥ 2 and for any linear homogeneous recurrence sequence {an}n≥1 satisfying certain conditions, there exits a positive constant c > 0 such that #{n ≤ x : an is palindromic in base b} x1−c.

We solve a 1985 challenge problem posed by Lagarias [5] by determining, under GRH, the density of the set of prime numbers that occur as divisor of some term of the sequence {xn}∞ n=1 defined by the linear recurrence xn+1 = xn + xn−1 and the initial values x0 = 3 and x1 = 1. This is the first example of a ‘non-torsion’ second order recurrent sequence with irreducible recurrence relation for whi...

* Correspondence: [email protected] Department of Basic Courses, Hebei Finance University, Baoding 071000, China Abstract This article is concerned with the following rational difference equation yn+1 = (yn + yn-1)/(p + ynyn-1) with the initial conditions; y-1, y0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the ...

Numeration systems the basis of which is defined b y a linear recurrence with integer coeficients are considered. W e give conditions on the recurrence under which the function of normalization which transforms any representation of an integer into the normal one obtained by the usual algorithm can be realized b y a finite automaton. Addition i s a particular case of normalization. The same que...

This paper investigates the number of spanning subgraphs of the product of an arbitrary graph G with the path graphs Pn on n vertices that meet certain properties: connectivity, acyclicity, Hamiltonicity, and restrictions on degree. A general method is presented for constructing a recurrence equation R(n) for the graphs G Pn, giving the number of spanning subgraphs that satisfy a given combinat...