On a family of sequences defined recursively in

We present a general class of recurrent systems which, under given initial conditions, generate infinite sequences in . In previous works (see Finite Fields Appl. 8 (2002) 91 and J. Number Theory 95 (2002) 268), we have seen that if (xi)i 1 is a sequence solution of such a system then the power series in defined by the continued fraction expansion [x1T,x2T,…,xnT,…] is algebraic over .