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A250752 Number of (n+1) X (5+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 A250752 #8 Nov 17 2018 20:55:09
%S A250752 294,957,3066,9633,29814,91317,277746,840873,2537934,7644477,22994826,
%T A250752 69107313,207567654,623194437,1870566306,5613664953,16844926974,
%U A250752 50542645197,151643664186,454962449793,1364950263894,4094976620757
%N A250752 Number of (n+1) X (5+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 A250752 R. H. Hardin, <a href="/A250752/b250752.txt">Table of n, a(n) for n = 1..210</a>
%F A250752 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (261*3^n - 120*2^n + 45)/2.
%F A250752 Empirical g.f.: 3*x*(98 - 269*x + 186*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e A250752 Some solutions for n=4:
%e A250752 ..1..1..1..1..1..1....0..0..0..0..0..0....1..1..1..1..1..2....2..2..2..2..2..2
%e A250752 ..0..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..2....0..0..0..0..0..0
%e A250752 ..0..0..0..0..1..1....2..2..2..2..2..2....0..0..0..0..0..1....2..2..2..2..2..2
%e A250752 ..0..0..0..0..1..1....1..1..1..1..1..1....0..0..0..0..0..2....2..2..2..2..2..2
%e A250752 ..1..1..1..1..2..2....0..1..2..2..2..2....0..0..0..0..0..2....0..0..1..2..2..2
%Y A250752 Column 5 of A250755.
%K A250752 nonn
%O A250752 1,1
%A A250752 _R. H. Hardin_, Nov 27 2014