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%I #7 Nov 15 2018 08:38:28
%S 57,140,297,592,1153,2236,4353,8528,16809,33292,66169,131824,263025,
%T 525308,1049745,2098480,4195801,8390284,16779081,33556496,67111137,
%U 134220220,268438177,536873872,1073745033,2147487116,4294971033
%N Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
%H R. H. Hardin, <a href="/A250606/b250606.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
%F Empirical: a(n) = 64*2^(n-1) + 5*n^2 + 4*n -16.
%F Empirical g.f.: x*(57 - 145*x + 110*x^2 - 32*x^3) / ((1 - x)^3*(1 - 2*x)). - _Colin Barker_, Nov 15 2018
%e Some solutions for n=6:
%e ..1..0..0..0....1..1..0..0....1..1..0..0....1..1..0..0....1..1..1..0
%e ..1..1..1..1....1..1..1..1....1..1..0..0....1..1..0..1....1..1..1..1
%e ..1..1..1..1....0..0..0..1....1..1..0..0....1..1..0..1....0..0..0..0
%e ..0..0..0..0....0..0..0..1....1..1..0..0....1..1..0..1....0..0..0..0
%e ..0..0..0..0....0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..0
%e ..1..1..1..1....0..0..0..1....0..0..0..0....0..0..0..1....1..1..1..1
%e ..0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..1
%Y Column 3 of A250611.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 26 2014
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