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A250543 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 x(i,j)-x(i-1,j) in the j direction.

%I A250543 #6 Jul 23 2025 12:31:42
%S A250543 4206453,64993652,555362165,3475227442,18064444143,83356429646,
%T A250543 355022719767,1430573448548,5544630982113,20906908229344,
%U A250543 77309801208801,281951865918318,1018337944028139,3653463640888634,13050682406346451
%N A250543 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 x(i,j)-x(i-1,j) in the j direction.
%C A250543 Column 7 of A250544
%H A250543 R. H. Hardin, <a href="/A250543/b250543.txt">Table of n, a(n) for n = 1..30</a>
%F A250543 Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)
%e A250543 Some solutions for n=1
%e A250543 ..0..0..2..1..2..0..1..0....0..0..0..0..1..0..0..0....0..2..2..0..2..0..0..0
%e A250543 ..0..0..2..1..2..1..2..3....0..0..0..0..1..3..3..3....0..3..3..1..3..1..3..3
%K A250543 nonn
%O A250543 1,1
%A A250543 _R. H. Hardin_, Nov 24 2014