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%I #8 Dec 10 2018 11:17:27
%S 47,132,306,742,1775,4158,9551,21591,48179,106371,232787,505683,
%T 1091603,2343699,5008403,10658835,22601747,47771667,100679699,
%U 211632147,443809811,928710675,1939603475,4043571219,8415870995,17489199123
%N Number of (n+1) X (2+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="/A253225/b253225.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>7.
%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)
%F G.f.: x*(47 - 103*x + 22*x^2 + 80*x^3 - 15*x^4 - 5*x^5 - 7*x^6) / ((1 - x)*(1 - 2*x)^2).
%F a(n) = 19 + 377*2^(n-6) + 627*2^(n-6)*n for n>4.
%F (End)
%e Some solutions for n=4:
%e ..0..1..0....0..1..0....0..0..1....0..1..1....1..1..0....0..1..0....1..1..1
%e ..1..1..1....0..1..1....0..0..0....0..1..1....1..1..1....1..1..0....1..1..1
%e ..0..0..0....1..1..1....1..1..0....0..1..1....0..0..0....0..1..1....0..0..0
%e ..1..1..1....1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1
%e ..1..1..1....1..0..1....0..0..0....1..0..1....0..0..1....1..1..1....0..0..1
%Y Column 2 of A253231.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2014
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