On recurrence sequences with polynomial coefficients (Q1372594)

Consider the sequence, \(A\), of rationals \(\{A_k\}\) generated by an \(n\)-term recurrence with polynomial coefficients and initial integer values: \(A_0\), \(A_1\), etc., \(A_{n-1}\). The author constructs an associated sequence \(\{H_k (A)\}\) such that if \(\{H_k (A)\}\) is bounded, then \(\{A_k\}\) is periodic with period \(t\). Furthermore, in this case, \(\{H_k (A)\}\) is bounded by a constant that is determined by \(n\), \(t\), and the \(n\) initial values of \(A\). The results given represent an improvement on similar prior results by van der Poorten and Shparlinski.