Abstract
Previous exact enumerations of the numbers and mean square lengths of short, first-neighbour-avoiding walks on the face-centred cubic, body-centred cubic and tetrahedral lattices have been extended to 12, 13 and 21 terms, respectively. Examination of the augmented data suggests an asymptotic expression for the mean square length of the form (Rn2) approximately An65/+Bnalpha . For the tetrahedral lattice this conjecture is supported by some new Monte Carlo data.