Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/11)

Mátyás Ferenc: Wythoff párok rekurzív sorozatok tagjaiból

- 27 MÁTYÁS FERENC WYTHOFF PÁROK REKURZÍV SOROZATOK TAGJAIBÓL Abstract: (Wythoff pairs with respect linear recurrences) - Let G=G |A, B, G

0, G

T }v,=o ^e a seconc

l order linear recurrence defined by integer constants A, B, G , G and the recurrence G = AG +BG Ol n n-in-2 Cn>l) where A

2+4B>0, G

2+G

2 & 0

. If a and ß are the ? o 1 roots of equation x

2-Ax-B=0 , then we have G

n

=

a <*

n-b /3

n * Many authors have discussed the properties of Wythoff pairs v

nj

> which are formed by letting u =1 and taking u

n as the smallest positive integer not yet used, and letting v «u^+n In this paper we deal with the connections between second order linear recurrences G and Wythoff pairs with respect linear recurrences which are defined by vn)

= í Í"

0^ integers with l^r<s, a is the root of polynomial x

2-Ax-B with the greatest absolute value and Cx3 denotes the integer part of the real number x. I. Definiáljuk a G=

G (A, B

F G

Q, G

T J

=-^G J másodrendű lineáris rekurzív sorozatot az A,B,G ,G rögzített egészekkel, melyekre LM] where r and s are fixed