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%I #7 Dec 16 2018 09:09:57
%S 636,1196,2088,3400,5136,7396,10236,13748,18024,23168,29292,36516,
%T 44968,54784,66108,79092,93896,110688,129644,150948,174792,201376,
%U 230908,263604,299688,339392,382956,430628,482664,539328,600892,667636,739848
%N Number of (n+2) X (4+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.
%H R. H. Hardin, <a href="/A253506/b253506.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/3)*n^4 + 6*n^3 + (329/3)*n^2 + 288*n - 12 for n>6.
%F Conjectures from _Colin Barker_, Dec 16 2018: (Start)
%F G.f.: 4*x*(159 - 496*x + 617*x^2 - 360*x^3 + 59*x^4 + 45*x^5 - 35*x^6 + 20*x^7 - 9*x^8 + 3*x^9 - x^10) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>11.
%F (End)
%e Some solutions for n=4:
%e ..1..1..1..1..1..1....0..1..1..1..1..0....1..1..1..1..1..1....0..1..1..1..1..1
%e ..1..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
%e ..1..1..1..1..1..0....1..1..1..1..0..1....1..1..1..1..0..0....1..1..1..1..1..1
%e ..1..1..1..1..0..0....1..1..1..1..0..1....1..1..1..1..1..1....1..1..1..1..1..1
%e ..1..1..0..1..0..1....1..1..1..1..0..1....1..1..0..0..0..0....1..1..0..0..0..0
%e ..1..0..0..1..0..1....1..0..0..0..0..1....1..1..0..1..1..1....1..0..1..1..1..1
%Y Column 4 of A253510.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
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