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%I #9 Nov 23 2018 03:17:48
%S 403,1325,4388,14196,44525,136509,412006,1231112,3657629,10837431,
%T 32088956,95066910,281997715,837788285,2492972738,7429400340,
%U 22170161033,66233321571,198057333352,592697831402,1774742767583,5316672917289
%N Number of (n+1) X (3+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="/A250893/b250893.txt">Table of n, a(n) for n = 1..210</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*(403 - 3511*x + 12668*x^2 - 24246*x^3 + 25568*x^4 - 13314*x^5 + 1284*x^6 + 1746*x^7 - 594*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).
%F a(n) = (-8*(179+223*2^n-25*3^(3+n)) + (1104-845*2^n)*n + (32+375*2^n)*n^2) / 32 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..1..2..1..1....1..1..0..0....2..1..0..1....2..2..1..0....2..0..1..0
%e ..0..1..0..0....1..2..1..1....1..2..1..2....2..2..2..1....2..0..1..2
%e ..1..2..1..2....1..2..1..1....1..2..1..2....1..1..1..0....2..0..1..2
%e ..1..2..1..2....0..1..0..0....1..2..1..2....1..1..1..1....2..0..1..2
%e ..0..1..0..1....0..2..2..2....1..2..1..2....1..1..1..2....2..0..1..2
%Y Column 3 of A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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