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%I #10 Nov 26 2018 11:44:00
%S 2129,4786,8050,14753,25597,46023,82431,151567,282371,536601,1033153,
%T 2013629,3956545,7822675,15528811,30912211,61642567,123062869,
%U 245854205,491382289,982373589,1964284511,3928022839,7855407543,15710071467
%N Number of (n+1) X (5+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="/A251134/b251134.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*(2129 - 7988*x + 7011*x^2 + 7381*x^3 - 16776*x^4 + 9606*x^5 - 883*x^6 - 571*x^7 + 21*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).
%F a(n) = (2*(5472+1058*(-1)^n+2809*2^n) + 6142*n + 1759*n^2 + 266*n^3 + 17*n^4) / 12 for n>3.
%F (End)
%e Some solutions for n=4:
%e ..2..0..0..0..0..2....0..0..0..0..0..0....2..2..2..2..2..2....0..0..0..0..0..0
%e ..2..0..0..0..0..2....1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0
%e ..2..0..0..0..0..2....0..0..0..0..0..0....2..2..2..2..2..2....0..0..0..0..0..0
%e ..2..0..0..0..0..2....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..2..0..0..0..0..0....2..2..1..1..1..1....2..1..1..1..1..0....2..1..1..1..1..1
%Y Column 5 of A251137.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
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