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%I #7 Nov 22 2018 08:24:05
%S 983950,5480917,20067117,57570016,140301126,303858745,601566177,
%T 1109545432,1932426406,3209691541,5122655965,7902083112,11836435822,
%U 17280762921,24666221281,34510233360,47427280222,64140330037,85492902061
%N Number of (7+1) X (n+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 R. H. Hardin, <a href="/A250859/b250859.txt">Table of n, a(n) for n = 1..23</a>
%F Empirical: a(n) = (15887/18)*n^6 + (39464/3)*n^5 + (2674189/36)*n^4 + (462227/2)*n^3 + (12645859/36)*n^2 + (743119/3)*n + 65536.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: x*(983950 - 1406733*x + 2363648*x^2 - 2238796*x^3 + 1326626*x^4 - 458751*x^5 + 65536*x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=1:
%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e ..0..0....0..0....0..0....0..0....2..2....1..1....1..1....1..1....1..1....2..2
%e ..3..3....2..3....2..2....2..2....0..0....2..2....0..0....2..3....0..0....0..0
%e ..2..3....1..2....3..3....0..0....2..2....2..2....1..1....1..2....1..1....3..3
%e ..2..3....1..2....2..2....1..3....0..1....2..2....1..1....1..2....0..0....1..2
%e ..1..3....1..3....2..2....1..3....0..1....1..2....1..2....0..2....3..3....2..3
%e ..0..2....1..3....0..0....1..3....0..1....2..3....2..3....1..3....1..1....1..2
%e ..1..3....1..3....0..2....0..3....1..2....0..3....0..1....0..2....0..0....0..2
%Y Row 7 of A250853.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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