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%I #9 Mar 19 2018 10:09:39
%S 16,58,209,746,2660,9476,33753,120216,428160,1524918,5431081,19343086,
%T 68891428,245360464,873864257,3112313708,11084669648,39478636370,
%U 140605248417,500773018002,1783529550852,6352134688572,22623463167433
%N Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.
%C Column 1 of A235517.
%H R. H. Hardin, <a href="/A235510/b235510.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 6*a(n-3) + a(n-4) + 2*a(n-5).
%F Conjectures from _Colin Barker_, Mar 19 2018: (Start)
%F G.f.: x*(16 - 6*x - 23*x^2 + 6*x^3 + 8*x^4) / ((1 - x)^2*(1 + x)*(1 - 3*x - 2*x^2)).
%F a(n) = (1/544)*(-221 - 68*(-1)^n + 2^(-1-n)*((2533-611*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(2533+611*sqrt(17))) - 68*(1+n)).
%F (End)
%e Some solutions for n=4:
%e ..1..1....1..1....1..0....0..0....1..0....0..1....1..0....0..1....1..0....0..0
%e ..1..0....0..1....0..0....1..1....1..1....1..1....1..0....1..0....1..1....0..0
%e ..0..1....0..1....1..1....1..0....1..0....0..0....1..1....1..1....0..0....0..1
%e ..1..1....0..1....1..0....1..0....1..1....1..0....1..0....0..0....1..1....1..1
%e ..0..0....0..1....1..0....1..0....1..0....0..1....0..0....1..1....1..1....0..0
%Y Cf. A235517.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
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