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%I #7 Dec 10 2018 12:18:53
%S 2470,4158,3241,4490,6414,9630,15363,26064,46635,86880,166407,324432,
%T 639387,1268136,2524407,5035656,10056795,20097648,40177863,80336736,
%U 160652859,321283416,642542775,1285059672,2570091579,5140153440
%N Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.
%H R. H. Hardin, <a href="/A253229/b253229.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.
%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)
%F G.f.: x*(2470 - 8192*x + 4681*x^2 + 8417*x^3 - 11033*x^4 + 3599*x^5 - 9*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).
%F a(n) = 1128 + 2451*2^(n-5) + 402*n + 33*n^2 for n>4.
%F (End)
%e Some solutions for n=4:
%e ..0..1..0..0..1..1..0....0..1..1..1..0..0..1....1..1..1..0..0..1..1
%e ..0..1..0..0..1..1..1....1..1..1..1..0..0..1....1..1..1..0..0..1..1
%e ..0..1..0..0..1..1..1....1..1..1..1..0..0..1....1..1..1..0..0..1..1
%e ..1..1..0..0..1..1..1....1..1..1..1..0..0..1....1..1..1..0..0..1..1
%e ..0..0..0..0..1..1..1....1..0..0..0..0..0..1....1..1..1..0..0..1..1
%Y Column 6 of A253231.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2014