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A250807 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 min(x(i,j),x(i-1,j)) in the j direction.

%I A250807 #8 Nov 20 2018 16:32:07
%S A250807 225,873,3081,10233,32745,102393,315561,963513,2924265,8840313,
%T A250807 26656041,80238393,241255785,724848633,2176708521,6534450873,
%U A250807 19612003305,58853311353,176594537001,529852816953,1589696862825,4769367412473
%N A250807 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 min(x(i,j),x(i-1,j)) in the j direction.
%H A250807 R. H. Hardin, <a href="/A250807/b250807.txt">Table of n, a(n) for n = 1..210</a>
%F A250807 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (304*3^n - 264*2^n + 66)/2.
%F A250807 Empirical g.f.: 3*x*(75 - 159*x + 106*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 20 2018
%e A250807 Some solutions for n=4:
%e A250807 ..2..2..2..1....2..2..2..2....2..1..0..0....2..2..2..2....0..0..0..0
%e A250807 ..1..1..1..1....2..2..2..2....0..0..0..0....0..0..0..0....0..0..0..0
%e A250807 ..1..1..1..1....2..2..2..2....1..1..1..1....1..1..1..1....0..0..0..1
%e A250807 ..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..0..0..1
%e A250807 ..0..0..0..0....0..1..2..2....0..0..1..1....0..1..1..1....0..0..0..2
%Y A250807 Column 3 of A250812.
%K A250807 nonn
%O A250807 1,1
%A A250807 _R. H. Hardin_, Nov 27 2014