I guess you are referring to the Honda EU3000ik model.
3000 watts (25 A) of Honda inverter 120 VAC power. ... The EU3000iKC is the latest addition to the popular Honda Inverter series of portable generators. The EU3000iKC adds increased portability to the durability, reliability and quiet operation of Honda’s existing EU3000isC generator ..
I think anything above 2400WATTS should do the 13,500BTU unit just fine. My EU2000i only really produces around 1850WATTS and this does not work with my 13,500BTU unit. The 3000Watt gen should only really produce around 2700WAtts so you should be in good shape...
Never know until you try it haha...
Roy Ken