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A250750 Number of (n+1) X (3+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 A250750 #8 Nov 17 2018 13:12:25
%S A250750 129,423,1353,4239,13089,40023,121593,367839,1109649,3341223,10048233,
%T A250750 30193839,90679809,272236023,817101273,2452090239,7357843569,
%U A250750 22076676423,66236320713,198721545039,596189800929,1788619734423,5365959866553
%N A250750 Number of (n+1) X (3+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 A250750 R. H. Hardin, <a href="/A250750/b250750.txt">Table of n, a(n) for n = 1..210</a>
%F A250750 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (114*3^n -48*2^n + 12)/2.
%F A250750 Empirical g.f.: 3*x*(43 - 117*x + 78*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e A250750 Some solutions for n=4:
%e A250750 ..1..1..1..1....0..0..0..0....0..0..0..0....2..2..2..2....1..1..1..1
%e A250750 ..2..2..2..2....1..1..1..2....1..1..1..1....1..1..1..1....0..0..0..0
%e A250750 ..1..1..1..1....0..1..1..2....2..2..2..2....1..1..1..2....2..2..2..2
%e A250750 ..1..1..1..1....0..1..1..2....2..2..2..2....0..0..0..1....1..1..1..1
%e A250750 ..0..1..2..2....0..1..1..2....0..1..2..2....0..0..0..1....1..1..1..2
%Y A250750 Column 3 of A250755.
%K A250750 nonn
%O A250750 1,1
%A A250750 _R. H. Hardin_, Nov 27 2014