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%I #8 Sep 05 2018 08:12:24
%S 0,15,0,113,0,427,0,1165,0,2591,0,5053,0,8947,0,14759,0,23017,0,34347,
%T 0,49409,0,68967,0,93813,0,124851,0,163005,0,209317,0,264843,0,330765,
%U 0,408271,0,498681,0,603315,0,723633,0,861087,0,1017275,0,1193781,0
%N Number of 5 X n -1,1 arrays such that the sum over i=1..5,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 5 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).
%H R. H. Hardin, <a href="/A225312/b225312.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-2) - 2*a(n-4) - 2*a(n-6) + 4*a(n-8) - 4*a(n-10) + 2*a(n-12) + 2*a(n-14) - 3*a(n-16) + a(n-18).
%F Empirical g.f.: x^2*(15 + 68*x^2 + 118*x^4 + 140*x^6 + 116*x^8 + 72*x^10 + 14*x^12 - 2*x^14 + x^16) / ((1 - x)^5*(1 + x)^5*(1 + x^2)^2*(1 + x^4)). - _Colin Barker_, Sep 05 2018
%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
%Y Row 5 of A225310.
%K nonn
%O 1,2
%A _R. H. Hardin_, May 05 2013
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