ON RATIONAL RECURSIVE SEQUENCES

We study the global asymptotic behavior, the oscillatory character, and the periodic nature of all positive solutions of the recursive sequences xn + 1 = (a + ∑k - 1 i = 0bixn - i)/xn - kn = 0, 1, 2, …, and xn + 1 = (a + bxn)/(A + xn - k), n = 0, 1, 2, …, where a, b, b0, …, bk - 1 and A are nonnegative numbers and k is a positive integer. © 1993 Academic Press, Inc.