# Counting the number of trainable parameters in a gradient boosted tree

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

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?