Number of 6Xn -1,1 arrays such that the sum over i=1..6,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 6 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).

A225313

Number of 6Xn -1,1 arrays such that the sum over i=1..6,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 6 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).