No, it is just 1. The core of the equation is counting “how often does the weight filter (aka kernel) fit onto the input”. Without padding and with stride=1, you get width_out = (width_in - filter_width) + 1. Now you can see where it comes from: If you start with width_in == filter_width, you have 1 possible position, and for each additional pixel column, i.e. one larger width_in, you have an additional position. So the 1 is this anchoring of the counting.
Best regards
Thomas