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A250757 Number of (2+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 A250757 #8 Nov 18 2018 07:38:46
%S A250757 105,237,423,663,957,1305,1707,2163,2673,3237,3855,4527,5253,6033,
%T A250757 6867,7755,8697,9693,10743,11847,13005,14217,15483,16803,18177,19605,
%U A250757 21087,22623,24213,25857,27555,29307,31113,32973,34887,36855,38877,40953,43083
%N A250757 Number of (2+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 A250757 R. H. Hardin, <a href="/A250757/b250757.txt">Table of n, a(n) for n = 1..210</a>
%F A250757 Empirical: a(n) = 27*n^2 + 51*n + 27.
%F A250757 Conjectures from _Colin Barker_, Nov 18 2018: (Start)
%F A250757 G.f.: 3*x*(35 - 26*x + 9*x^2) / (1 - x)^3.
%F A250757 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250757 (End)
%e A250757 Some solutions for n=4:
%e A250757 ..1..1..1..1..1....2..2..2..2..2....1..2..2..2..2....1..2..2..2..2
%e A250757 ..0..1..1..1..1....0..0..1..1..1....0..2..2..2..2....1..2..2..2..2
%e A250757 ..0..1..1..1..1....0..0..2..2..2....0..2..2..2..2....0..1..1..2..2
%Y A250757 Row 2 of A250755.
%K A250757 nonn
%O A250757 1,1
%A A250757 _R. H. Hardin_, Nov 27 2014