Check the soundex codes. Many times when people arrived in the new world, the names were altered by the local immigration authorities who often were barely literate. It you don't know what the soundex codes are, they are names that sound like Larsen (in your case) that are spelled differently.
The reason I say to check that is because on the Binkley side of my family, it originated in Switzerland as Binggeli. So if you soundex search on Binggeli, Binkley, Binkly, Brinkley etc all come up with quite a few others. That can sometimes lead to clues from the home countries. Was Andrew an immigrant, or was it his descendants that immigrated? If he was the immigrant, there are databases of passenger manifests online and in other places.