- a settlement puts down one +3 structure and runs it at +3 in month #1 (the rest of the structures are low or missing)
- the current actual settlement level is 10 that week

Then the "Adjusted Settlement Level" for that one +3 structure will be the current Settlement Level of 10 plus 6 more for double "structure plus", less the 3, which give a interim result of 10+6-3=13. We then subtract 1 for being month 1 and get an "Adjusted Settlement Level" of 12 meaning our +3 structure will train and have a facility rating equivalent to a level 12 settlement?

Since it's a +3 structure, it will always run at least at the equivalent of a level 16 settlement, so the adjusted settlement level can be ignored in this case (+0=10, +1=12, +2=14, +3=16, +4=18, +5=20). However, if the settlement level ran at 15 during month #1 (which just to be clear is actually the second month, we're using programmer math here where counting starts at zero), then the adjusted settlement level would be 17 (15+6-3-1=17), so the +3 structure would run like it would now in a level 17 settlement (sort of like a +3.5). Likewise, if the settlement level was 18, then the +3 structure would run like a +5 (level 20) structure during that month, dropping by a level each month until it hit that minimum of 16.