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A250818 Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250818 #7 Nov 21 2018 08:04:13
%S A250818 13449,42769,102393,207831,377857,634509,1003089,1512163,2193561,
%T A250818 3082377,4216969,5638959,7393233,9527941,12094497,15147579,18745129,
%U A250818 22948353,27821721,33432967,39853089,47156349,55420273,64725651,75156537,86800249
%N A250818 Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H A250818 R. H. Hardin, <a href="/A250818/b250818.txt">Table of n, a(n) for n = 1..203</a>
%F A250818 Empirical: a(n) = 136*n^4 + 1225*n^3 + 4402*n^2 + 5499*n + 2187.
%F A250818 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250818 G.f.: x*(13449 - 24476*x + 23038*x^2 - 10934*x^3 + 2187*x^4) / (1 - x)^5.
%F A250818 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A250818 (End)
%e A250818 Some solutions for n=3:
%e A250818 ..0..0..0..0....2..2..2..2....1..1..1..0....1..1..1..1....2..1..2..2
%e A250818 ..1..1..1..1....0..0..0..0....0..0..0..0....1..1..1..1....1..1..2..2
%e A250818 ..2..2..2..2....0..0..0..0....0..0..0..1....2..2..2..2....1..1..2..2
%e A250818 ..0..0..0..0....2..2..2..2....1..1..1..2....2..2..2..2....1..1..2..2
%e A250818 ..0..0..0..0....1..1..1..1....1..1..1..2....1..1..1..2....1..1..2..2
%e A250818 ..2..2..2..2....0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1
%e A250818 ..0..1..2..2....1..1..2..2....0..1..1..2....1..1..1..2....0..0..2..2
%Y A250818 Row 6 of A250812.
%K A250818 nonn
%O A250818 1,1
%A A250818 _R. H. Hardin_, Nov 27 2014