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A250811 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 min(x(i,j),x(i-1,j)) in the j direction.

%I A250811 #8 Nov 20 2018 16:32:31
%S A250811 2025,8049,29145,98481,318585,1003089,3104985,9507441,28908345,
%T A250811 87498129,264041625,795220401,2391853305,7187945169,21588607065,
%U A250811 64815365361,194545185465,583833736209,1751897569305,5256485430321,15771041736825
%N A250811 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 min(x(i,j),x(i-1,j)) in the j direction.
%H A250811 R. H. Hardin, <a href="/A250811/b250811.txt">Table of n, a(n) for n = 1..210</a>
%F A250811 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (3016*3^n - 3024*2^n + 1050)/2.
%F A250811 Empirical g.f.: 3*x*(675 - 1367*x + 1042*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 20 2018
%e A250811 Some solutions for n=4:
%e A250811 ..2..2..2..1..0..0..0..0....2..2..2..1..1..1..0..0....2..2..2..2..2..2..2..2
%e A250811 ..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....1..1..1..1..1..1..1..1
%e A250811 ..1..1..2..2..2..2..2..2....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
%e A250811 ..1..1..2..2..2..2..2..2....1..1..1..1..2..2..2..2....1..1..2..2..2..2..2..2
%e A250811 ..0..0..1..1..1..1..1..2....0..0..1..1..2..2..2..2....0..0..1..1..1..1..1..1
%Y A250811 Column 7 of A250812.
%K A250811 nonn
%O A250811 1,1
%A A250811 _R. H. Hardin_, Nov 27 2014