Wavelet Packet Decomposition: How many coefficients on a certain level?

From the theory of wavelet packet decomposition, I understood that if I have a number of N samples of the input signal, on a level L I get 2^L sets of coefficients, each set with N/2^L coefficients.

So I decompose my signal which has 1024 samples with wpdec on 7 levels using db4 and on level 7 I was expecting to find 8 coefficients in each set (I use wpcoef to get the coefficients), but instead I have 14 coefficients in each set. Moreover, if I use another type of wavelet, I get a different number of coefficients on level 7 (for db1, I get 16 coefficients).

Can someone please explain this difference between the theory and what I get in Matlab and also how do different wavelets influence the number of coefficients on each level? Thank you! (As a disclaimer, I'm new to the field of wavelets, so I may have not understood everything very well.)