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A250754 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 x(i,j)+x(i-1,j) in the j direction.

%I A250754 #8 Nov 17 2018 20:55:00
%S A250754 527,1707,5471,17211,53327,163467,497471,1506651,4548527,13702827,
%T A250754 41223071,123898491,372154127,1117379787,3353974271,10065592731,
%U A250754 30204118127,90627034347,271910463071,815790109371,2447487768527
%N A250754 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 x(i,j)+x(i-1,j) in the j direction.
%H A250754 R. H. Hardin, <a href="/A250754/b250754.txt">Table of n, a(n) for n = 1..210</a>
%F A250754 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (468*3^n - 224*2^n + 98)/2.
%F A250754 Empirical g.f.: x*(527 - 1455*x + 1026*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e A250754 Some solutions for n=4:
%e A250754 ..1..1..1..1..1..1..1..1....2..2..2..2..2..2..2..1....0..0..0..0..0..0..0..0
%e A250754 ..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..2....1..1..1..1..1..1..1..1
%e A250754 ..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..2....0..0..0..0..0..0..1..1
%e A250754 ..1..2..2..2..2..2..2..2....0..0..0..0..0..0..0..1....0..0..0..0..0..0..1..1
%e A250754 ..0..1..1..1..1..2..2..2....0..0..0..0..0..0..0..1....0..0..0..0..0..0..1..2
%Y A250754 Column 7 of A250755.
%K A250754 nonn
%O A250754 1,1
%A A250754 _R. H. Hardin_, Nov 27 2014