First granted in 1721, Allenstown was named after Samuel Allen, governor of the province while still under the jurisdiction of Massachusetts just prior to 1700. A portion of Bow was annexed to the town in 1815, and a portion of Hooksett in 1853. The area was once known as excellent bear country, and a good hunting ground for wild geese and ducks. Allenstown is home to Bear Brook State Park, the largest developed state park in New Hampshire, according to the NH Division of Parks and Recreation. The park covers nearly 10,000 acres and offers historical museums along with recreational swimming, hiking, biking, camping, and fishing.
Population change for Allenstown totaled 2,509 over 56 years, from 1,789 in 1960 to 4,298 in 2016. The largest decennial percent change was a 61 percent increase between 1970 and 1980, which followed a 53 percent increase over the previous decade. The 2016 Census estimate for Allenstown was 4,298 residents, which ranked 87th among New Hampshire's incorporated cities and towns.(info from NHES website)