Some invariants for κth-order Lyness equation

Abstract We present the second and third invariants for the k th -order Lyness equation, x n +1 = a + x n + x n−1 + … + x n−κ + 2/x n−κ+1 , n = 0, 1, , 1 where the parameter a is an arbitrary positive number. These invariants are functionally independent.