We present new evolutionary sequences for low and intermediate mass stars ( 1 M _ { \odot } to 6 M _ { \odot } ) for three different metallicities , Z = 0.02 , 0.008 and 0.004 .
We evolve the models from the pre-main sequence to the thermally-pulsing asymptotic giant branch phase .
We have two sequences of models for each mass , one which includes mass loss and one without mass loss .
Typically 20 or more pulses have been followed for each model , allowing us to calculate the third dredge-up parameter for each case .
Using the results from this large and homogeneous set of models , we present an approximate fit for the core mass at the first thermal pulse , M _ { c } ^ { 1 } , as well as for the third dredge-up efficiency parameter , \lambda , and the core mass at the first dredge-up episode , M _ { c } ^ { min } , as a function of metallicity and total mass .
We also examine the effect of a reduced envelope mass on the value of \lambda .