%I
%S 133,416,1002,2264,4786,9786,19548,38674,76196,150192,296626,587420,
%T 1166206,2320222,4623712,9225118,18421072,36804772,73562342,147065944,
%U 294059610,588031298,1175956612,2351786634,4703423196,9406669816
%N Number of (n+1) X (2+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="/A251131/b251131.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n1)  13*a(n2) + 10*a(n3) + 5*a(n4)  14*a(n5) + 9*a(n6)  2*a(n7) for n>9.
%F Conjectures from _Colin Barker_, Nov 26 2018: (Start)
%F G.f.: x*(133  382*x + 235*x^2 + 330*x^3  597*x^4 + 264*x^5 + 27*x^6  26*x^7  4*x^8) / ((1  x)^5*(1 + x)*(1  2*x)).
%F a(n) = (873 + 49*(1)^n + 841*2^(1+n)  614*n  11*n^2 + 38*n^3 + 5*n^4) / 12 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..1..1..1....0..0..2....0..1..2....0..0..2....0..0..1....0..0..2....0..1..2
%e ..0..0..0....1..0..2....1..0..0....2..0..2....0..0..1....0..0..0....0..0..0
%e ..1..1..1....2..0..2....1..0..0....2..0..2....1..1..1....0..0..0....1..0..0
%e ..1..0..0....2..0..2....2..0..0....2..0..1....0..0..0....0..0..0....1..0..0
%e ..2..0..0....2..0..1....2..0..0....2..0..0....0..0..0....2..1..1....1..0..0
%Y Column 2 of A251137.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
