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

Bogdan Tropak: Some algebraic properties of linear recurrences

- 76 n-Ct-mJ _ y X

t 4 2 C b a t -1 m n t =1 m+n^l O^m^r t=l m=0 n=0 n^t -m k o .n-Ct -rrO 1 c 2 x, « 1 b a m t -- 1 n m = 0 l = m + 1 n = t -rn The last, equality follows from the fact that for t£m we have a o 7 b a

r,t "

m = a

m_

t 2 b a

n = a

wt u(a) = 0. n n n = I - rn n = 0 Now, changing the order of summation and understanding u^x) similarly as g(x) in C3) we obtain es r r z = 5 a

n~

p J c I X, = a n rn •*- t -1 p = l n = p m = 0 t =rn + 1 t -m=p 2 u Ca) J c X ^ = p m p -1 p = 1 m = 0 2 2 ( ^r -m^p-1 +mj ^ U p = i in — O p = 1 Ca) Z „ p p-i Analogously for ß being a root of vCx) we obtain ''ft = I v

tC/» Y l=i