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Number of (n+1) X (6+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.

Column 6 of A250611

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

Empirical: a(n) = 196*2^(n-1) + 99*n^2 + 177*n + 30.

Empirical g.f.: 2*x*(251 - 669*x + 447*x^2 - 128*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018

Some solutions for n=6:

Column 6 of A250611.

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R. H. Hardin, <a href="/A250609/b250609.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (n+1)X(6+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

502, 1172, 2236, 3890, 6526, 10928, 18664, 32870, 59818, 112052, 214660, 417818, 821878, 1627544, 3236224, 6450734, 12876706, 25725404, 51419356, 102803618, 205568302, 411093632, 822140056, 1644228470, 3288400666, 6576740228

1,1

Column 6 of A250611

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

Empirical: a(n) = 196*2^(n-1) +99*n^2 +177*n +30

Some solutions for n=6

..1..0..1..1..0..1..0....1..1..1..1..1..0..0....0..0..0..0..0..0..0

..1..0..1..1..0..1..1....0..0..0..0..1..0..0....1..1..1..1..1..1..1

..0..0..1..1..0..1..1....0..0..0..0..1..0..0....0..0..0..0..0..0..0

..0..0..1..1..0..1..1....0..0..0..0..1..0..0....1..1..1..1..1..1..1

..0..0..1..1..0..1..1....0..0..0..0..1..0..1....1..1..1..1..1..1..1

..0..0..1..1..0..1..1....0..0..0..0..1..0..1....0..0..0..0..0..0..0

..0..0..1..1..0..1..1....0..0..0..0..1..0..1....0..0..0..1..1..1..1

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nonn

R. H. Hardin, Nov 26 2014

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