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%I #6 Aug 19 2022 13:44:17
%S 0,0,22,122,0,0,29638,197440,0,0,64811436,458450486,0,0,170747302728,
%T 1245085560292,0,0,497500354657954,3694982212755606,0,0,
%U 1544103180477715700,11609994393282630090,0,0,5004924971984927428464
%N Number of n X 7 -1,1 arrays such that the sum over i=1..n, j=1..7 of i*x(i,j) is zero and rows are nondecreasing (ways to put 7 thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate).
%C Column 7 of A225310.
%H R. H. Hardin, <a href="/A225308/b225308.txt">Table of n, a(n) for n = 1..210</a>
%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..1
%e .-1.-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..1
%e ..1..1..1..1..1..1..1...-1.-1.-1..1..1..1..1...-1.-1.-1.-1..1..1..1
%Y Cf. A225310.
%K nonn
%O 1,3
%A _R. H. Hardin_, May 05 2013
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