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%I #8 Nov 17 2018 20:55:18
%S 402,1305,4182,13149,40722,124785,379662,1149669,3470442,10454265,
%T 31448742,94518189,283898562,852383745,2558527422,7678334709,
%U 23040509082,69132537225,207419631702,622302935229,1866996886002,5601166818705
%N Number of (n+1) X (6+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 R. H. Hardin, <a href="/A250753/b250753.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (357*3^n - 168*2^n + 69)/2.
%F Empirical g.f.: 3*x*(134 - 369*x + 258*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 17 2018
%e Some solutions for n=4:
%e ..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..1..1..1
%e ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....1..1..1..1..2..2..2
%e ..2..2..2..2..2..2..2....2..2..2..2..2..2..2....0..0..0..0..1..1..1
%e ..0..1..1..2..2..2..2....2..2..2..2..2..2..2....1..1..1..1..2..2..2
%e ..0..1..1..2..2..2..2....0..0..0..0..0..0..1....0..0..0..1..2..2..2
%Y Column 6 of A250755.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014
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