%I #7 Nov 21 2018 14:52:33
%S 54410,291165,1043885,2955136,7134786,15344785,30214465,55486360,
%T 96292546,159461501,253855485,390738440,584174410,851456481,
%U 1213566241,1695663760,2327608090,3144508285,4187304941,5503382256,7147210610
%N Number of (5+1) X (n+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 R. H. Hardin, <a href="/A250857/b250857.txt">Table of n, a(n) for n = 1..176</a>
%F Empirical: a(n) = (763/18)*n^6 + (1949/3)*n^5 + (136493/36)*n^4 + (72691/6)*n^3 + (693923/36)*n^2 + (43319/3)*n + 4096.
%F Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F G.f.: x*(54410 - 89705*x + 148340*x^2 - 141944*x^3 + 83994*x^4 - 28671*x^5 + 4096*x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=1:
%e ..2..2....2..2....1..1....3..3....3..3....3..3....2..1....3..3....3..2....0..1
%e ..3..3....0..1....3..3....0..1....3..3....3..3....0..1....3..3....1..1....1..2
%e ..2..2....0..1....3..3....2..3....3..3....3..3....0..1....2..2....2..3....1..2
%e ..2..2....0..1....1..1....0..1....2..2....0..0....0..1....1..1....0..1....1..2
%e ..0..1....1..3....3..3....2..3....2..2....1..1....2..3....0..1....1..2....0..1
%e ..0..2....1..3....1..1....2..3....0..1....2..2....0..3....0..2....0..3....0..2
%Y Row 5 of A250853.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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