I recently ran the gradient boosted tree regressor using scikit-learn via:

GradientBoostingRegressor()

This model depends on the following hyperparameters:

• Estimators ($N_1$)
• Min Samples Leaf ($N_2$)
• Max Depth ($N_3$) which in-turn determine the number of trainable parameters in this model. My question is, how can I count the number of parameters (trainable or otherwise randomly assigned) which determined the final model as a function of the above?

My guess is $N_1 \times N_2 \times N_3$ but is this correct?