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%I #8 Nov 23 2018 08:47:42
%S 413,1450,4388,12387,33821,91030,244200,657443,1784205,4894210,
%T 13588116,38193131,108619621,312200310,905600200,2647025819,
%U 7785177061,23009431986,68264323652,203115146611,605677397453,1809046090230
%N Number of (3+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%H R. H. Hardin, <a href="/A250901/b250901.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
%F Empirical g.f.: x*(413 - 4332*x + 19193*x^2 - 47217*x^3 + 70990*x^4 - 67269*x^5 + 39526*x^6 - 13236*x^7 + 1944*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 23 2018
%e Some solutions for n=4:
%e ..0..1..1..1..1....2..1..0..1..0....2..2..2..0..0....2..2..0..1..1
%e ..0..1..1..1..1....1..0..1..2..1....2..2..2..1..1....2..2..1..2..2
%e ..0..1..1..1..1....1..0..1..2..2....2..2..2..1..1....1..1..0..1..1
%e ..0..1..1..2..2....1..0..1..2..2....1..1..1..0..2....0..0..1..2..2
%Y Row 3 of A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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