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

Molnár Sándor: Lineáris rekurzív sorozatok egy eloszlási tulajdonságáról

_ 3 H. MOLNÁR SÁNDOR* LINEÁRIS REKUZÍV SOROZATOK EGY ELOSZLÁSI TULAJDONSÁGÁRÓL Abstract: (On a distribution property of linear reccurences) Let G= Í

G 1 n be a second order linear recurrence of real numbers n

) n = O defined by the recursion G =AG +BG 0 for n£2 , where A J nn-ln-2 ' and B are non-zero real numbers and the initial terms G

Q , G C^CO are given. The distribution properties of these sequences have been studied by several authors. For example Tichy showed that there are infinitely many sequences G which are everywhere dense modulo 1 on the unit interval but they not uniformly distributed. However the characteristic plynomials of the sequences in Tichy's construction have positive discriminants. In present paper we extend this result for sequences having negative discriminants furthermore we give the asymptotic distribution functions, too. * A kutatást (részben) az Országos Tudományos Kutatási Alap 273. sz. pályázata támogatta.