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%I #7 Sep 05 2018 06:13:39
%S 2,7,16,31,52,83,122,175,238,317,410,523,650,801,970,1165,1380,1625,
%T 1892,2193,2518,2879,3268,3697,4154,4655,5188,5767,6380,7043,7742,
%U 8495,9286,10133,11022,11971,12962,14017,15118,16285,17500,18785,20120,21529,22990
%N Number of 4 X n -1,1 arrays such that the sum over i=1..4,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 4 positions 1..n distance from the hinge of a south-pointing gate without turning the gate).
%H R. H. Hardin, <a href="/A225311/b225311.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).
%F Empirical g.f.: x*(2 + 5*x + 7*x^2 + 8*x^3 + 5*x^4 + 4*x^5 + x^6 + 2*x^7 + x^8 - x^9) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _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
%Y Row 4 of A225310.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 05 2013
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