Parameter counting with Design Matrices

[pstevens]

I am attempting to constrain phi, p and b to be the same within weeks but different between weeks using the design matrix and the POPAN formulation (I need population estimates). However, this has gotten me confused on how many estimable parameters I actually have. The data represents 1-6 sampling sampling events per week over a total of 22 weeks. According to my understanding of the "Gentle Intro," K should be equal to 22 since I am constraining parameters within weeks. Therefore for the fully time dependent model I should have estimable parameters as follows:

3K-3 = 3(22)-3 = 63 estimable parameters

Is this correct or do I still need to use the total number of sampling events (n=94) as my K value?