Number of 7Xn -1,1 arrays such that the sum over i=1..7,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 7 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

A225314

Number of 7Xn -1,1 arrays such that the sum over i=1..7,j=1..n of i*x(i,j) is zero and rows are nondecreasing (ways to put n thrusters pointing east or west at each of 7 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).