Generating functions for products of recursive sequences
David Zeitlin · Transactions of the American Mathematical Society · 1965
(1.4) u0= 1, ul = p, Un = PUn-1 qun-2 (n = 2, 3, ...), (1.5) v0= 2, vl = p, Vn = PVn-1 qvn-2 (n = 2, 3, ...), with p2 4q # 0. In (1.3a) and (1.3b) (which are the generating functions for the kth power of two special second order sequences), Uk(x) and Vk(x) are polynomials in x of degree ? k for k ? 1, and Dk(x) is a polynomial in x of degree k + 1. It should be pointed out that the desired form for Dk(x) [3, p. 530, (6.5)] in terms of ar (i.e., our (2.4) with m = 1) is given, with a