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A250758 Number of (3+1) X (n+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 A250758 #8 Nov 18 2018 09:06:18
%S A250758 332,756,1353,2123,3066,4182,5471,6933,8568,10376,12357,14511,16838,
%T A250758 19338,22011,24857,27876,31068,34433,37971,41682,45566,49623,53853,
%U A250758 58256,62832,67581,72503,77598,82866,88307,93921,99708,105668,111801,118107
%N A250758 Number of (3+1) X (n+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 A250758 R. H. Hardin, <a href="/A250758/b250758.txt">Table of n, a(n) for n = 1..210</a>
%F A250758 Empirical: a(n) = (173/2)*n^2 + (329/2)*n + 81.
%F A250758 Conjectures from _Colin Barker_, Nov 18 2018: (Start)
%F A250758 G.f.: x*(332 - 240*x + 81*x^2) / (1 - x)^3.
%F A250758 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250758 (End)
%e A250758 Some solutions for n=4:
%e A250758 ..1..1..2..2..2....2..2..2..2..2....1..1..1..1..1....0..0..0..0..0
%e A250758 ..0..0..1..1..1....0..0..0..1..1....2..2..2..2..2....0..0..0..0..0
%e A250758 ..0..0..1..1..1....0..0..0..1..1....0..0..0..0..2....2..2..2..2..2
%e A250758 ..0..0..1..1..1....0..0..0..1..2....0..0..0..0..2....0..0..0..1..1
%Y A250758 Row 3 of A250755.
%K A250758 nonn
%O A250758 1,1
%A A250758 _R. H. Hardin_, Nov 27 2014