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A250849 Number of (n+1) X (4+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 A250849 #8 Nov 21 2018 09:17:43
%S A250849 3136,21436,123016,626416,2955136,13263136,57570016,244213216,
%T A250849 1019415136,4206874336,17218194016,70050978016,283750743136,
%U A250849 1145667917536,4614715410016,18555090670816,74509245399136,298904020992736
%N A250849 Number of (n+1) X (4+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 A250849 R. H. Hardin, <a href="/A250849/b250849.txt">Table of n, a(n) for n = 1..210</a>
%F A250849 Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (52650*4^n - 80640*3^n + 35820*2^n - 2688)/12.
%F A250849 Empirical g.f.: 4*x*(784 - 2481*x + 4604*x^2 - 2571*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 21 2018
%e A250849 Some solutions for n=3:
%e A250849 ..3..3..1..1..1....3..3..2..2..3....2..2..1..1..1....2..1..1..1..1
%e A250849 ..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....1..1..1..1..1
%e A250849 ..0..0..0..0..1....0..0..1..2..3....0..0..2..2..2....1..1..1..1..1
%e A250849 ..0..0..0..1..2....0..0..1..2..3....0..1..3..3..3....0..0..1..2..3
%Y A250849 Column 4 of A250853.
%K A250849 nonn
%O A250849 1,1
%A A250849 _R. H. Hardin_, Nov 28 2014