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A250851 Number of (n+1) X (6+1) 0..3 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 A250851 #8 Nov 21 2018 11:26:50
%S A250851 14400,103293,614965,3204951,15344785,69543783,303858745,1294875471,
%T A250851 5422612945,22429374423,91953454825,374560079391,1518555885505,
%U A250851 6135323831463,24724903375705,99451052025711,399459752428465
%N A250851 Number of (n+1) X (6+1) 0..3 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 A250851 R. H. Hardin, <a href="/A250851/b250851.txt">Table of n, a(n) for n = 1..210</a>
%F A250851 Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (282492*4^n - 462196*3^n + 224994*2^n - 20568)/12.
%F A250851 Empirical g.f.: x*(14400 - 40707*x + 86035*x^2 - 49444*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 21 2018
%e A250851 Some solutions for n=2:
%e A250851 ..1..1..0..1..1..1..1....3..3..2..3..3..3..3....3..3..2..2..1..1..1
%e A250851 ..0..0..0..1..2..3..3....0..0..1..2..2..2..2....0..0..0..0..0..0..0
%e A250851 ..0..0..0..1..2..3..3....0..0..1..2..2..3..3....1..1..1..1..3..3..3
%Y A250851 Column 6 of A250853.
%K A250851 nonn
%O A250851 1,1
%A A250851 _R. H. Hardin_, Nov 28 2014