%I #4 May 05 2013 06:39:55
%S 0,35,0,443,0,2341,0,8221,0,22351,0,51521,0,105247,0,196779,0,342979,
%T 0,565693,0,891247,0,1352233,0,1986519,0,2839617,0,3963039,0,5417341,
%U 0,7269805,0,9598181,0,12487593,0,16035169,0,20345971,0,25538619,0
%N 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)
%C Row 6 of A225310
%H R. H. Hardin, <a href="/A225313/b225313.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-2) +a(n-4) -a(n-10) -2*a(n-14) +a(n-18) +a(n-20) +a(n-22) +a(n-24) -2*a(n-28) -a(n-32) +a(n-38) +a(n-40) -a(n-42)
%e Some solutions for n=4
%e .-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1.-1....1..1..1..1
%e .-1.-1..1..1....1..1..1..1....1..1..1..1...-1.-1.-1.-1...-1..1..1..1
%e ..1..1..1..1...-1.-1.-1.-1...-1.-1.-1..1...-1.-1.-1.-1...-1.-1.-1.-1
%e .-1..1..1..1...-1.-1.-1.-1...-1.-1..1..1...-1.-1.-1..1...-1.-1.-1.-1
%e .-1.-1.-1..1...-1.-1..1..1...-1..1..1..1....1..1..1..1....1..1..1..1
%e .-1.-1.-1..1....1..1..1..1...-1.-1.-1..1...-1..1..1..1...-1.-1..1..1
%K nonn
%O 1,2
%A _R. H. Hardin_ May 05 2013