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Number of (n+1) X (5+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 #7 Nov 15 2018 08:38:42

%S 247,586,1153,2092,3691,6526,11749,21664,40879,78610,153289,301780,

%T 597811,1188838,2369773,4730440,9450487,18889210,37765201,75515644,

%U 151014907,302011726,604003573,1207985392,2415947071,4831868386

%N Number of (n+1) X (5+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="/A250608/b250608.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 Empirical: a(n) = 144*2^(n-1) + 42*n^2 + 69*n - 8.

%F Empirical g.f.: x*(247 - 649*x + 446*x^2 - 128*x^3) / ((1 - x)^3*(1 - 2*x)). - _Colin Barker_, Nov 15 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Column 5 of A250611.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014