with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...

We investigate the properties of recurrence of the type xn+1 = (a+ ∑k−2 i=0 xn−i)/xn−(k−1), known as Lyness iterations from [Lyness, 1942, 1945, 1961] and recently analyzed by several authors in the case a > 0, see e.g. [Kocic et al., 1993; Csornyei & Laczkovich, 2000]. We reconsider Lyness recurrences at the light of some recent results on iterated maps with denominator, given in [Bischi et al...

We study various matrix models with a charge-charge interaction as toy models of the gauge dual of the AdS black hole. These models show a continuous spectrum and power-law decay of correlators at late time and infinite N , implying information loss in this limit. At finite N , the spectrum is discrete and correlators have recurrences, so there is no information loss. We study these models by a...

The mesh-connected computer with multiple buses (MCCMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2-D generalized MCCMB (2-GMCCMB) for the purpose of increasing the efficiency of executing some important applications of prefix computations such as solving linear recurrences and tridiagonal systems, etc. A klnl ...

where the A{ are rational integers, is called an integral linear recurrence of order k. Given such a linear recurrence and an integer c, one would like to know for what n does f(n) — c? In a very few particular instances (e.g. see [2], [6]) this question has been answered, but in general the question is very difficult. A less exacting problem is the determination of upper and lower bounds on th...

Denote by sq(w) the number of distinct squares in a string w and let S be the class of standard Sturmian words. They are generalizations of Fibonacci words and are important in combinatorics on words. For Fibonacci words the asymptotic behaviour of the number of runs and the number of squares is the same. We show that for Sturmian words the situation is quite different. The tight bound 8 10 |w|...

(4) vn = vl + r». To c o n t i n u e , we need t h e fo l lowing d e f i n i t i o n s which a r e modeled a f t e r t h e n o t a t i o n of Hal ton [3] . The l e t t e r p w i l l always denote a r a t i o n a l p r ime . Vd^nAJtton I : v ( a , b9 p) i s t h e numeric of t h e PR u(a9 b) modulo p . I t i s the number of n o n r e p e a t i n g terms modulo p . Vt^AJbitiovi 2°> ] i (a , b9 p) ...

In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]

We introduce new recurrences for the type B and type D Eulerian polynomials, and interpret them combinatorially. These recurrences are analogous to a well-known recurrence for the type A Eulerian polynomials. We also discuss their relationship to polynomials introduced by Savage and Visontai in connection to the real-rootedness of the corresponding Eulerian polynomials.

Motivated by questions of algorithm analysis, we provide several distinct approaches to determining convergence and limit values for a class of linear iterations.