CARATUNK — Neither Eric Angevine nor his son Zachary have hiked the Appalachian Trail, but they have no shortage of stories from life on the 2,200-mile footpath. There were the five hikers who stole the ice cream supply at the Sterling Inn, where the Angevines are the innkeepers; the couple who arrived with no money to pay for their stay and surreptitiously camped in the backyard; the city-slicker who offered to work in order to pay for his stay but had to be taught how to use a lawnmower; and the pair of high school sweethearts suspected of hitchhiking between camps while their parents paid for their “hike.” “There are lots of funny people that come through here and most of them that you meet are great,” said Eric Angevine, 67. The father-son duo, who took over the inn in 2012, are part of a long-standing tradition of hospitality at the big white house on a desolate stretch of U.S.