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%I #7 Nov 23 2018 05:37:45
%S 32095,88421,244200,680504,1893433,5232461,14283986,38498188,
%T 102731213,272597111,722672320,1922589386,5152218779,13948044421,
%U 38216305022,106061750888,298128374761,848068491251,2438292434012,7074745440934
%N Number of (n+1) X (7+1) 0..2 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="/A250897/b250897.txt">Table of n, a(n) for n = 1..196</a>
%F Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.
%F Conjectures from _Colin Barker_, Nov 23 2018: (Start)
%F G.f.: x*(32095 - 296719*x + 1108848*x^2 - 2144026*x^3 + 2239408*x^4 - 1181770*x^5+ 162292*x^6 + 174146*x^7 - 73990*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).
%F a(n) = -17515/4 + 4833*2^(-1+n) + (198025*3^(-3+n))/4 + (23737/2-28323*2^(-5+n))*n + (5071+53217*2^(-5+n))*n^2 for n>2.
%F (End)
%e Some solutions for n=2:
%e ..2..2..0..0..1..0..0..1....2..1..1..2..1..1..0..0....1..1..0..1..0..1..0..1
%e ..2..2..0..0..1..0..0..1....1..0..0..1..0..2..1..1....1..1..0..2..1..2..1..2
%e ..2..2..0..0..2..1..1..2....1..0..0..1..0..2..2..2....1..1..0..2..1..2..1..2
%Y Column 7 of A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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