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A225306 Number of nX5 -1,1 arrays such that the sum over i=1..n,j=1..5 of i*x(i,j) is zero and rows are nondecreasing (ways to put 5 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).

%I A225306 #6 Jun 02 2025 08:31:55
%S A225306 0,0,12,52,0,0,5304,26498,0,0,3670280,19472528,0,0,3059952646,
%T A225306 16735288748,0,0,2821236602612,15715467775786,0,0,2770728141476684,
%U A225306 15624859528160442,0,0,2841704521905480868,16166720093745817028,0,0
%N A225306 Number of nX5 -1,1 arrays such that the sum over i=1..n,j=1..5 of i*x(i,j) is zero and rows are nondecreasing (ways to put 5 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 A225306 Column 5 of A225310
%H A225306 R. H. Hardin, <a href="/A225306/b225306.txt">Table of n, a(n) for n = 1..210</a>
%e A225306 Some solutions for n=4
%e A225306 ..1..1..1..1..1...-1.-1.-1..1..1...-1.-1.-1..1..1....1..1..1..1..1
%e A225306 .-1.-1.-1.-1.-1...-1.-1.-1..1..1...-1..1..1..1..1...-1..1..1..1..1
%e A225306 .-1.-1.-1.-1.-1....1..1..1..1..1....1..1..1..1..1...-1.-1.-1.-1.-1
%e A225306 ..1..1..1..1..1...-1.-1.-1.-1..1...-1.-1.-1.-1.-1...-1.-1..1..1..1
%K A225306 nonn
%O A225306 1,3
%A A225306 _R. H. Hardin_ May 05 2013