On the periodicity of the sequence xn+1 = max{A0/xn, A1/xn-1,..., Ak/xn-k}

We give a complete characterization of the behaviour of the sequence cited in the title with negative coefficients, i.e. we settle Conjecture 2.3.2 and Problem 2.3.1, and give a partial answer for Problem 2.3.2 of Ladas (J. Difference Equ. and Appl. 2 (1996) 339-341). We also give a similar argument for an already known result for the case when all the coefficients have the same fixed positive value.