In this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polyno¬mials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painleve equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients.