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%I #10 Dec 11 2018 08:59:54
%S 125,724,4800,30920,199512,1285960,8289288,53433608,344449224,
%T 2220470152,14314275912,92277661448,594874191816,3834903188104,
%U 24722024949576,159372675116552,1027409972582088,6623289504223624,42697625485315656
%N Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal maximum minus antidiagonal maximum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
%H R. H. Hardin, <a href="/A253345/b253345.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) - 8*a(n-2) - 72*a(n-3) + 96*a(n-4) + 128*a(n-5) - 128*a(n-6) - 64*a(n-7) for n>8.
%F Empirical g.f.: x*(125 - 401*x - 716*x^2 + 2512*x^3 - 240*x^4 - 2192*x^5 + 512*x^6 + 512*x^7) / ((1 - 2*x)*(1 - 2*x - 4*x^2)*(1 - 5*x - 12*x^2 + 16*x^3 + 8*x^4)). - _Colin Barker_, Dec 11 2018
%e Some solutions for n=4:
%e ..1..1..1..1....1..0..0..0....1..1..1..1....0..0..0..1....0..0..1..1
%e ..0..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1....0..0..1..0
%e ..0..1..0..0....1..0..0..1....0..0..0..0....0..1..1..1....0..0..1..1
%e ..0..1..0..0....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..0
%e ..1..1..1..1....0..0..1..1....0..0..1..0....1..1..1..0....0..1..1..1
%Y Column 3 of A253350.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2014