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%I #7 Nov 18 2018 09:00:25
%S 35,62,114,216,418,820,1622,3224,6426,12828,25630,51232,102434,204836,
%T 409638,819240,1638442,3276844,6553646,13107248,26214450,52428852,
%U 104857654,209715256,419430458,838860860,1677721662,3355443264
%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 absolute value of x(i,j)-x(i-1,j) in the j direction.
%H R. H. Hardin, <a href="/A250764/b250764.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 25*2^(n-1) + 2*n + 8.
%F Empirical g.f.: x*(35 - 78*x + 41*x^2) / ((1 - x)^2*(1 - 2*x)). - _Colin Barker_, Nov 18 2018
%e Some solutions for n=4:
%e ..0..1..0..1....0..0..0..0....0..0..0..0....1..1..1..0....0..0..0..0
%e ..0..1..0..1....0..1..1..1....0..0..0..0....1..1..1..0....0..0..0..0
%e ..0..1..0..1....0..1..1..1....1..1..1..1....1..1..1..0....0..0..0..0
%e ..0..1..0..1....0..1..1..1....0..0..0..0....1..1..1..1....0..0..0..1
%e ..0..1..0..1....0..1..1..1....0..0..0..0....1..1..1..1....0..0..0..1
%Y Column 3 of A250769.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014