Quantization: levels or intervals?
Peak signal to quantisation noise ratio (I think that's what you mean by PSQNR?) is a rather unusual thing to calculate for signal converters. If you are truly interested in the peak signal and noise, then that comes out as 1.5delta for your example, and counting the intervals is relevant.

What we normally do in signal processing (radio, radar, audio, that sort of thing) where the energy of the signal is all important, is to use rms. It's useful to think about the signal potentially going a little beyond the peak converter levels, and so counting the levels is more appropriate.

Of course, when you get to practical word sizes, N being say 4 or more, the difference between \$2^N\$ and \$2^N-1\$ becomes insignificant.

Be very careful you understand which measure, peak or rms, your various text books are using, and why. Also check whether they are just making a large N assumption.