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A250749 Number of (n+1) X (2+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 A250749 #8 Nov 17 2018 13:12:00
%S A250749 72,237,756,2361,7272,22197,67356,203601,613872,1847757,5555556,
%T A250749 16691241,50122872,150466917,451597356,1355185281,4066342272,
%U A250749 12200599677,36604944756,109821125721,329475960072,988453046037,2965409469756
%N A250749 Number of (n+1) X (2+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 A250749 R. H. Hardin, <a href="/A250749/b250749.txt">Table of n, a(n) for n = 1..210</a>
%F A250749 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (63*3^n - 24*2^n + 3)/2.
%F A250749 Empirical g.f.: 3*x*(24 - 65*x + 42*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e A250749 Some solutions for n=4.
%e A250749 ..2..2..1....2..2..2....2..2..2....0..0..0....0..0..0....2..2..2....2..2..2
%e A250749 ..0..0..1....0..0..0....2..2..2....1..1..1....1..1..1....2..2..2....1..1..1
%e A250749 ..0..0..2....1..1..1....1..1..1....1..1..1....0..0..0....2..2..2....1..2..2
%e A250749 ..0..0..2....1..1..1....1..1..2....2..2..2....1..1..2....1..1..1....1..2..2
%e A250749 ..0..0..2....1..1..1....1..1..2....1..1..2....1..1..2....1..1..1....0..2..2
%Y A250749 Column 2 of A250755.
%K A250749 nonn
%O A250749 1,1
%A A250749 _R. H. Hardin_, Nov 27 2014