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A250523 Number of (n+1)X(4+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 A250523 #7 Nov 14 2018 14:05:23
%S A250523 3123,18859,82023,300131,993123,3088923,9240559,26984403,77707851,
%T A250523 222271083,634724183,1815888579,5216209523,15062616251,43743061503,
%U A250523 127741126963,374944674139,1105460634123,3271582279911,9712201092643
%N A250523 Number of (n+1)X(4+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 A250523 R. H. Hardin, <a href="/A250523/b250523.txt">Table of n, a(n) for n = 1..210</a>
%F A250523 Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
%F A250523 Empirical g.f.: x*(3123 - 24863*x + 83452*x^2 - 163338*x^3 + 214295*x^4 - 196963*x^5 + 119218*x^6 - 39828*x^7 + 5832*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 14 2018
%e A250523 Some solutions for n=3:
%e A250523 ..2..2..1..1..0....0..1..1..0..0....2..0..0..0..0....2..1..2..1..1
%e A250523 ..1..1..1..1..0....1..2..2..2..2....1..0..0..1..2....1..0..1..0..0
%e A250523 ..0..0..1..2..1....0..1..1..1..1....1..0..0..1..2....0..0..1..0..0
%e A250523 ..0..0..1..2..1....0..1..2..2..2....1..0..0..1..2....0..0..1..0..2
%Y A250523 Column 4 of A250527.
%K A250523 nonn
%O A250523 1,1
%A A250523 _R. H. Hardin_, Nov 24 2014