%I #10 Nov 26 2018 11:44:28
%S 4699,9786,15830,27738,46023,79226,135959,240780,434193,804400,
%T 1519053,2920510,5684595,11169870,22084427,43851224,87307005,
%U 174131892,347676817,694650138,1388459119,2775924642,5550678879,11099992388,22198396553
%N Number of (n+1) X (6+1) 0..2 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.
%H R. H. Hardin, <a href="/A251135/b251135.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 10*a(n-3) + 5*a(n-4) - 14*a(n-5) + 9*a(n-6) - 2*a(n-7) for n>10.
%F Conjectures from _Colin Barker_, Nov 26 2018: (Start)
%F G.f.: x*(4699 - 18408*x + 18201*x^2 + 12986*x^3 - 35970*x^4 + 22238*x^5 - 2915*x^6 - 1012*x^7 + 39*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).
%F a(n) = (9*(3271+441*(-1)^n+441*2^(1+n)) + 15178*n + 4111*n^2 + 578*n^3 + 35*n^4) / 12 for n>3.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0..0..0..2....0..1..1..1..1..1..1....0..0..0..2..0..0..2
%e ..0..0..0..0..0..0..1....0..0..0..0..0..0..0....0..0..0..2..0..0..2
%e ..0..0..0..0..0..0..1....0..0..0..0..0..0..0....1..0..0..2..0..0..0
%e ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....2..0..0..2..0..0..0
%e ..2..2..2..2..1..1..0....2..1..1..1..0..0..0....2..0..0..2..0..0..0
%Y Column 6 of A251137.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014