How are you defining "distinct conflicts"? The 1890 census states that "The Indian wars under the government of the United States have been more than 40 in number." For an example of how defining an "Indian war" is difficult, let's look at the Navajos. War between the Navajo and the United States lasted from 1846-1864, but there were only a few big, official expeditions into Navajo country. Otherwise it was a cycle of raids and reprisals, as had existed with first the Pueblo, then the Spanish, and then Mexican resident of New Mexico for hundreds of years. Did the U.S. wage one war against the Navajo, or many small wars?