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A250751 Number of (n+1) X (4+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 A250751 #8 Nov 17 2018 16:25:21
%S A250751 203,663,2123,6663,20603,63063,191723,580263,1751003,5273463,15861323,
%T A250751 47665863,143161403,429811863,1290090923,3871583463,11617371803,
%U A250751 34857358263,104582560523,313768653063,941347902203,2824127592663
%N A250751 Number of (n+1) X (4+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 A250751 R. H. Hardin, <a href="/A250751/b250751.txt">Table of n, a(n) for n = 1..210</a>
%F A250751 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (180*3^n - 80*2^n + 26)/2.
%F A250751 Empirical g.f.: x*(7 - 9*x)*(29 - 42*x) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e A250751 Some solutions for n=4:
%e A250751 ..2..2..2..2..2....2..2..2..2..2....1..1..1..1..1....0..0..0..0..0
%e A250751 ..2..2..2..2..2....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
%e A250751 ..1..1..1..1..1....0..1..1..1..1....1..2..2..2..2....0..0..0..0..0
%e A250751 ..0..0..0..0..0....1..2..2..2..2....0..1..1..1..1....1..1..1..1..2
%e A250751 ..0..0..0..1..2....0..1..2..2..2....0..1..1..1..2....1..1..1..1..2
%Y A250751 Column 4 of A250755.
%K A250751 nonn
%O A250751 1,1
%A A250751 _R. H. Hardin_, Nov 27 2014