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A250852 Number of (n+1) X (7+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 A250852 #8 Nov 21 2018 11:26:46
%S A250852 27225,198297,1195457,6279401,30214465,137379337,601566177,2567402601,
%T A250852 10763029505,44552408777,182750596897,744705474601,3020091585345,
%U A250852 12204496276617,49191016683617,197884445031401,794901482169985
%N A250852 Number of (n+1) X (7+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 A250852 R. H. Hardin, <a href="/A250852/b250852.txt">Table of n, a(n) for n = 1..210</a>
%F A250852 Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (562288*4^n - 939120*3^n + 470064*2^n - 45220)/12.
%F A250852 Empirical g.f.: x*(27225 - 73953*x + 165362*x^2 - 96024*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 21 2018
%e A250852 Some solutions for n=2:
%e A250852 ..3..2..2..2..1..1..1..1....1..1..1..1..0..0..0..0....3..2..0..1..1..1..1..1
%e A250852 ..0..0..0..1..1..1..1..1....0..0..0..0..0..0..0..1....0..0..0..1..1..1..1..1
%e A250852 ..0..0..0..2..2..3..3..3....0..0..0..0..0..0..0..3....0..1..1..2..2..3..3..3
%Y A250852 Column 7 of A250853.
%K A250852 nonn
%O A250852 1,1
%A A250852 _R. H. Hardin_, Nov 28 2014