Number of city-block distance 1, pressure limit 2 movements in an n X n array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops.

A216984

Number of city-block distance 1, pressure limit 2 movements in an n X n array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops.