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A250808 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 min(x(i,j),x(i-1,j)) in the j direction.

%I A250808 #8 Nov 20 2018 16:32:14
%S A250808 441,1731,6171,20631,66291,207831,641571,1961031,5955891,18013431,
%T A250808 54331971,163579431,491905491,1478051031,4438822371,13325805831,
%U A250808 39996095091,120025640631,360151632771,1080604320231,3242111804691
%N A250808 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 min(x(i,j),x(i-1,j)) in the j direction.
%H A250808 R. H. Hardin, <a href="/A250808/b250808.txt">Table of n, a(n) for n = 1..210</a>
%F A250808 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (620*3^n - 570*2^n + 162)/2.
%F A250808 Empirical g.f.: 3*x*(147 - 305*x + 212*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 20 2018
%e A250808 Some solutions for n=4:
%e A250808 ..2..2..2..1..2....2..1..0..0..0....1..1..1..1..1....1..1..1..1..1
%e A250808 ..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....1..1..1..1..1
%e A250808 ..0..0..0..0..1....0..0..0..1..1....1..1..1..1..2....0..0..0..1..1
%e A250808 ..0..0..1..1..2....1..1..1..2..2....0..0..0..0..1....0..0..0..1..1
%e A250808 ..0..0..1..1..2....0..0..0..2..2....0..1..1..1..2....0..0..0..1..1
%Y A250808 Column 4 of A250812.
%K A250808 nonn
%O A250808 1,1
%A A250808 _R. H. Hardin_, Nov 27 2014