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%I #8 Nov 20 2018 08:16:16
%S 576,1596,4054,10306,25126,59590,137082,307762,676266,1460260,3107536,
%T 6535280,13611742,28129720,57764876,118015794,240116940,486922786,
%U 984765176,1987317314,4003558184,8054089024,16184388422,32492334224
%N Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%H R. H. Hardin, <a href="/A250789/b250789.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 35*a(n-3) - 9*a(n-4) - 37*a(n-5) + 47*a(n-6) - 15*a(n-7) - 10*a(n-8) + 9*a(n-9) - 2*a(n-10).
%F Empirical g.f.: 2*x*(288 - 1506*x + 2843*x^2 - 1193*x^3 - 3324*x^4 + 5009*x^5 - 1866*x^6 - 1087*x^7 + 1094*x^8 - 256*x^9) / ((1 - x)^6*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Nov 20 2018
%e Some solutions for n=4:
%e ..1..0..0..0..0....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
%e ..1..0..0..0..0....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
%e ..1..0..0..0..1....1..0..0..1..0....0..0..1..0..1....0..0..0..0..0
%e ..1..0..0..0..1....1..0..1..0..1....0..1..0..1..0....0..0..0..0..0
%e ..1..0..0..1..0....1..0..1..0..1....0..1..0..1..1....0..0..0..0..1
%e ..1..0..0..1..0....1..0..1..0..1....0..1..0..1..1....0..0..0..1..0
%e ..1..0..1..0..1....1..1..0..1..0....0..1..0..1..1....0..1..1..0..1
%e ..1..1..0..1..0....1..1..0..1..1....0..1..0..1..1....0..1..1..0..1
%Y Row 7 of A250783.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014
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