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A250847 Number of (n+1) X (2+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 A250847 #9 Nov 21 2018 09:17:51
%S A250847 400,2457,13097,63631,291165,1280447,5480917,23024631,95448605,
%T A250847 391939087,1598379237,6485763431,26220548845,105716192127,
%U A250847 425369781557,1709000211031,6858576189885,27502054979567,110211518943877
%N A250847 Number of (n+1) X (2+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 A250847 R. H. Hardin, <a href="/A250847/b250847.txt">Table of n, a(n) for n = 1..210</a>
%F A250847 Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (4838*4^n - 6300*3^n + 2214*2^n - 80)/12.
%F A250847 Empirical g.f.: x*(400 - 1543*x + 2527*x^2 - 1344*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 21 2018
%e A250847 Some solutions for n=4:
%e A250847 ..3..1..1....1..1..1....2..2..3....0..0..0....2..1..1....3..1..1....3..3..2
%e A250847 ..0..0..0....3..3..3....2..2..3....1..1..1....1..1..1....1..1..1....0..0..0
%e A250847 ..2..2..3....2..2..3....2..2..3....1..1..1....1..1..1....0..1..1....0..0..0
%e A250847 ..0..1..3....0..0..1....2..2..3....1..2..2....0..0..0....0..2..3....0..1..2
%e A250847 ..0..1..3....1..2..3....0..1..2....0..1..2....2..3..3....0..2..3....1..2..3
%Y A250847 Column 2 of A250853.
%K A250847 nonn
%O A250847 1,1
%A A250847 _R. H. Hardin_, Nov 28 2014