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%I #8 Dec 11 2018 08:59:38
%S 6740,9551,6231,8216,11022,15363,22656,35736,60273,107607,200418,
%T 384066,749271,1477473,2931552,5837268,11646141,23261211,46488558,
%U 92940342,185840883,371638821,743231436,1486413288,2972773497,5945490303
%N Number of (n+1) X (7+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="/A253230/b253230.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 11 2018: (Start)
%F G.f.: x*(6740 - 24149*x + 19136*x^2 + 15840*x^3 - 27356*x^4 + 9682*x^5 - 11*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).
%F a(n) = (3/32)*(25728 + 945*2^n + 9200*n + 624*n^2) for n>4.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....0..1..1..1..1..1..1..1
%e ..0..0..0..0..0..0..0..0....1..1..1..1..1..0..0..0....0..0..0..0..0..0..0..0
%e ..1..1..1..1..1..1..1..1....1..1..1..1..1..0..0..0....1..1..1..1..1..1..1..1
%e ..0..0..0..0..0..0..0..0....1..0..0..0..0..0..0..0....1..0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0..1....1..0..0..0..0..1..1..1....1..0..0..0..0..0..0..1
%Y Column 7 of A253231.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2014
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