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Number of (n+1) X (7+1) 0..1 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.
1

%I #8 Nov 15 2018 11:07:39

%S 1013,2336,4353,7320,11749,18664,30113,50192,87093,157200,293281,

%T 560872,1091045,2145944,4249857,8451360,16847605,33632896,67195841,

%U 134313656,268540773,536986056,1073867233,2147619760,4295114549,8590093424

%N Number of (n+1) X (7+1) 0..1 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.

%H R. H. Hardin, <a href="/A250610/b250610.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

%F Conjectures from _Colin Barker_, Nov 15 2018: (Start)

%F G.f.: x*(1013 - 2729*x + 1790*x^2 - 512*x^3) / ((1 - x)^3*(1 - 2*x)). - _Colin Barker_, Nov 15 2018

%F a(n) = 128 + 2^(7+n) + 410*n + 219*n^2.

%F (End)

%e Some solutions for n=6:

%e ..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..0....1..1..1..1..0..1..0..0

%e ..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0

%e ..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0

%e ..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0

%e ..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0

%e ..0..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0

%e ..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..1..1

%Y Column 7 of A250611.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014